International Journal of Impact Engineering 36 (2009) 1044–1057
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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Crash response of advanced high-strength steel tubes: Experiment and model Nader Abedrabbo a, *, Robert Mayer b, Alan Thompson a, Christopher Salisbury a, Michael Worswick a, Isadora van Riemsdijk c a
Department of Mechanical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada General Motors Research & Development Center, Warren, MI 48090, USA c Dofasco Inc. (ArcelorMittal), Research & Development, Hamilton, ON L8N 3J5, Canada b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 March 2008 Received in revised form 1 December 2008 Accepted 21 February 2009 Available online 4 March 2009
The performance of non-hydroformed and hydroformed structural steel tubes in component-level crash testing was investigated using both experimental and analytical techniques. In particular, the focus was on high-strength steels that may have potential to enhance crashworthiness of automobiles. Monolithic tubes made from multiple materials and wall thicknesses were considered in this study. The following materials were used: conventional drawing quality (DDQ) steels; high-strength low alloy (HSLA-350) steels; and advanced high-strength steel (AHSS) materials comprising the dual phase alloys DP600 and DP780. The goal of this research was to study the interaction between the forming and crash response of these materials in order to evaluate their potential for use in vehicle design for crashworthiness. The tubes were hydroformed using two methods known as low- and high-pressure processes. Material characterization of all materials was carried out through quasi-static and high strain rate tensile tests in the range of 0.00333–1500 s1, and rate sensitive constitutive models for all materials were developed. The nonlinear explicit dynamic finite element code LS-DYNA, in conjunction with the validated constitutive models, was used to simulate both the hydroforming processes and the crash tests performed on the tubes. The energy absorption characteristics of the different tubes were calculated and the results from the numerical analyses were compared against the experimental data. This comparison was performed in order to determine whether the interactions between forming and crush could be adequately predicted using finite element analysis. The effects of thickness changes, work hardening, and component geometry, which resulted from hydroforming, on the crash response were also investigated. A study of the significance of strain rate and the importance of performing detailed material characterization on the accuracy of the numerical analysis was performed. Also, a parametric study on the effect of transferring forming history data between simulations on the accuracy of the numerical analysis was performed, and the importance of carrying forward the histories between multiple forming simulations was demonstrated. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Crashworthiness Tube hydroforming High-strength steels Formability Energy absorption
1. Introduction There is a strong motivation in the automotive sector to increase vehicle fuel efficiency. One important method of achieving this goal is the use of lightweight structures [1–6]. At the same time, however, these new lighter structures must maintain or exhibit improved crash energy absorption. Multiple candidates for replacing mild steel in automotive structures have been proposed such as advanced high-strength steels, aluminum or magnesium alloys, and composite materials. Advanced high-strength steels (AHSSs), in particular, are attractive candidate materials, offering
* Corresponding author. Tel.: þ1 713 983 5147; fax: þ1 713 983 5040. E-mail address:
[email protected] (N. Abedrabbo). 0734-743X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2009.02.006
higher strength for energy absorption and the opportunity to reduce weight through use of thinner gauges. However, though mild steels are highly formable, the increase in strength achieved using AHSS materials is at the expense of a reduction in formability. Thus, there is a need to address the formability of high-strength steel tubes. In addition, the history of the forming processes performed on these materials influences the behaviour of the final component in the impact test. Therefore, it is important to study the energy absorption characteristics of advanced high-strength steels in the as-formed condition during crash testing. Multiple research articles have been published on the subject of axial crushing of steel sections. White and Jones [7,8] explored the collapse features of top-hat and double-hat sections made of mild steel when subjected to axial crushing. Abramowicz et al. [9–11] studied the dynamic axial crushing of circular and square steel
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tubes and compared the results with theoretical predictions. Schneider and Jones [3] investigated the impact of thin-walled high-strength steel sections made into top-hat and square highstrength steel sections and compared the results with those of mild steel sections. Tube hydroforming (THF) technology has become a popular method, especially in the automotive industry, for producing complex three-dimensional structural shapes. There are several advantages to hydroforming over conventional processes such as stamping and welding. These advantages include part consolidation, weight reduction due to improved part design, improved structural strength and stiffness, and reduction in the associated tooling and material costs [12]. In view of these advantages, the range of parts currently being produced or developed using THF by the automotive industry continues to grow. These parts include engine cradles, radiator supports, roof side rails, exhaust manifold assemblies, camshafts, sub-frames and instrument support panels [13,14]. Two methods are widely used to hydroform circular tubes: low-pressure (low-expansion) and high-pressure (high-expansion) hydroforming processes. A key difference between the two processes is that the low-pressure process introduces only limited circumferential expansion with little or no end-feeding required to form the tube. In the high-pressure method, the circumferential strains are large, causing thinning of the tube, and therefore endfeeding of the tube (extra tube material pushed into the die) is used to counteract thinning. Numerical optimization linked with the finite element method was used in order to determine the optimum pressure and end-feeding profiles required to successfully hydroform the different tubes with the high-pressure process. Details of the optimization process with the developed profiles are presented by Abedrabbo et al. [15]. Numerical analysis is a critical tool for understanding the complex deformation mechanics that occur during forming and impact processes. Finite element analysis (FEA) is used in automotive design and formability processes to predict deformation behaviour accurately during stamping and crash testing. Finite element method (FEM) simulation of the hydroforming process, for example, has been proven to be an advantageous tool in assisting automotive designs. The numerical method used in this research utilized the ‘‘carry forward’’ method in which forming history data are transferred from one simulation to the next. This is a critical step in order to ensure the accuracy of the numerical results when compared to the experimental ones. The purpose of this research was to study the interaction between the hydroforming process and crash test response of multiple advanced high-strength steel monolithic tubes. Also, another goal was to assess and compare the performance of AHSS tubes in a crash event. The research focused on axial crush structures that are designed to absorb crash energy by progressive axial folding. Experiments were performed in which the hydroforming process parameters were varied in a parametric fashion and the crash test response was measured. The experimental parameters varied included: tube thickness, hydroformed corner-fill tube radii, and consideration of the so-called ‘low’ vs. ‘high’ pressure processes. The dimensions of the corner-fill radii used to form the tubes were 6 mm and 18 mm. Impact testing of non-hydroformed tubes, low-pressure hydroformed tubes and high-pressure hydroformed tubes was conducted using a deceleration track-sled apparatus. Numerical studies were carried out using explicit dynamic finite element models to capture the entire forming and crash test histories. Another important step in the research was to verify the accuracy of the previously developed material models [16] in order to evaluate their use in the design processes. From the experimental and numerical results, several important predictions about
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the energy absorption capabilities of the various steels were made. Of particular importance were the predictions involving the advanced high-strength steels. 2. Materials In the current research, monolithic tubes made from a range of steels and wall thicknesses were considered. All of the tubes in this research had an outer diameter of 76.2 mm, and were made using a tube rolling process with induction seam welding. The materials investigated include the following: conventional deep drawing quality (DDQ) steel of wall thickness 1.8 mm; high-strength low alloy (HSLA-350) steel with wall thicknesses of 1.5 mm and 1.8 mm; and advanced high-strength steel (AHSS) materials comprising the dual phase alloys DP600 with wall thickness of 1.8 mm and DP780 with wall thickness of 1.5 mm. High-strength low alloy (HSLA) and dual phase (DP) steels are currently being used to reduce the weight of automobiles. Not only do they show good strength, formability and weldability, but also their cost is lower than equivalent heat-treated alloys because they achieve their desired characteristics directly from hot rolling [17]. Dual phase (DP) steels are essentially low-carbon steels that contain a large amount of manganese (1–2 wt. %) and silicon (0.05–0.2 wt. %) as well as small amounts of microalloying elements, such as vanadium, titanium, molybdenum, and nickel. 2.1. Constitutive equations (flow stress) Material characterization was performed on the different materials used in this research [16,18,19] in order to extract the required parameters of the constitutive models for the purpose of numerical analysis. The materials were tested in both the sheet and the as-formed tube conditions in order to identify the effect of the tube forming operation on the tube properties. For the as-formed tube material, testing was performed on specimens from three positions on the perimeter of the tube, corresponding to the 3, 6, and 9 o’clock positions (the weld seam is located at 12 o’clock), as shown in Fig. 1. In order to characterize the materials throughout the complete range of strain rates seen in a crash event, uniaxial tensile experiments were conducted on each material at strain rates ranging from 0.00333 s1 to 1500 s1. The low strain rate tests (0.00333– 0.1 s1) were conducted using a servo-controlled tensile machine.
Weld Seam 12 O’clock
Tensile Sample
3 O’clock
9 O’clock
6 O’clock Fig. 1. Top view of cross section of the tube showing locations of test samples used in tensile tests and the location of the weld seam.
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The intermediate strain rate tests (30–100 s1) were carried out using an instrumented falling weight impact machine, while the high rate tests (500–1500 s1) were carried out using a tensile split Hopkinson bar (TSHB). Comprehensive details about the material characterization procedure and the results for all materials presented in this paper can be found in Thompson et al. [16], Winkler et al. [18] and Smerd et al. [19]. From these tensile tests, the parameters of two constitutive models (flow stress models) were fit to the experimental results for each material. The first is the Power-Law model which is used to simulate the hydroforming process, forming of the crush initiators, and trimming of the as-formed tubes. This model is represented as:
sð3p Þ ¼ Kð3p þ 30 Þn ;
(1)
where ‘‘K’’ (strength hardening coefficient) and ‘‘n’’ (strain-hardening exponent) are material constants. 3p is the effective plastic strain and 30 is a constant representing the elastic strain at yield. In the impact part of the experiments, strain rates vary over a large range. Also, due to heat from plastic deformation, the adiabatic temperature increases in the material, resulting in material softening. For these reasons, the Johnson–Cook model [20], which incorporates these two effects, was used in the numerical analysis of impact. This constitutive model is typically used in impact analysis and vehicle crash simulations and is available in commercial finite element codes, such as the LS-DYNA finite element code which was used in the current research. The Johnson–Cook constitutive model is represented as follows:
n
sð3p Þ ¼ a þ b3p
1 þ c ln 3_ *
m 1 T* ;
(2)
where a, b, c, n and m are material constants. 3p is the effective plastic strain. 3_ * ¼ 3_ =30 is the effective deviatoric strain rate normalized by the quasi-static threshold rate. The value of the quasi-static threshold rate represents the highest strain rate for which no rate adjustment to the flow stress is needed [21]. T* is the homologous temperature and is given by:
T* ¼
T Troom Tmelt Troom
(3)
where T is the current temperature of the material, Troom is room temperature, and Tmelt is the melting temperature of the steel. Although multiple tensile tests were performed for each material in different directions (sheet data, 3, 6, and 9 o’clock tube positions), and the constitutive parameters were calculated for each direction, only one set of parameters is used in the numerical analysis. In order to represent the tube in its multiple directions in the numerical analysis, a weighted average method was used to calculate the constitutive parameters for the two models. The following formula was used:
Xavg ¼
2*X3o0 clock þ X6o0 clock 3
(4)
where X represents a general variable. This specific averaging method was used because tensile test results indicated that the work hardening imparted to the tube during the tube manufacturing process is symmetric but not uniform. Therefore, the 3 and 9 o’clock positions were found to be very close and thus considered equal. Table 1 lists the constitutive parameters of the Power-Law model, while Table 2 lists the constitutive parameters of the Johnson–Cook model for all the materials used in the research. Fig. 2 shows a sample of the measured true stress vs. true strain for all the materials used in this research. The figure shows the data for the tube materials in the 3 o’clock position. Figs. 3 and 4 show a sample of the strain rate results, in this case for the DP780
Table 1 Constitutive parameters of the Power-Law model for the different tubular materials used. Material
t0 (mm)
OD (mm)
K (MPa)
n
30
DDQ HSLA-350 HSLA-350 DP-600 DP-780
1.8 1.5 1.8 1.8 1.5
76.2 76.2 76.2 76.2 76.2
578.1 684.0 679.9 900.0 1166.4
0.183 0.095 0.121 0.109 0.130
7.46E 4 1.81E 3 1.49E 3 2.24E 3 2.60E 3
material, at room temperature and strain rates from 0.003 s1 to 1360 s1 tested in the sheet and 3 o’clock position, respectively. 3. Experimental procedure 3.1. Tube hydroforming Circular tubes were hydroformed using two methods: the lowexpansion (low-pressure) and high-expansion (high-pressure) hydroforming processes. A key difference between these two processes is that the low-pressure process introduces only limited circumferential expansion with no end-feeding required to form the tube. In the high-pressure method, the circumferential strains are large, causing excessive tube thinning to occur. In order to counter the thinning problem, end-feeding of the tube, where extra tube material is pushed into the die cavity, was used. Hydroforming of the circular tubes was performed using squareshaped dies with two different corner radii inserts: 6 mm and 18 mm. Tubes were hydroformed using a 1000 tonne (9806.65 kN) Macrodyne hydroforming press at the University of Waterloo labs [15]. To illustrate the differences between the two types of hydroforming processes typically used in THF, Fig. 5 shows a comparison between the low- and high- pressure tubes at the end of the hydroforming process. Also shown in the graph is the original tube size (round shape) used in the two types of experiments before hydroforming. In the low-pressure (LP) hydroforming process, the initial tube diameter is larger than the sectional diameter of the die cavity. As the die closes, it mechanically forms the tube to the die shape under a small internal fluid pressure present to prevent buckling or pinching. After the die is closed, the fluid pressure is gradually increased to form the tube. In the high-pressure (HP) hydroforming process, the tube is initially in contact with the sides of the die, as shown in Fig. 5. As fluid pressure is increased, tube expansion occurs to fill the corner areas. In the HP case, no mechanical forming occurs before fluid pressure is applied. As seen in Fig. 5, the high-pressure process causes higher expansion of the tube (between 18% and 26% change in perimeter, depending on corner radius) compared to the low-pressure process (approximately 0.8% change in perimeter). In order for the tubes to be hydroformed using the high-pressure process, i.e. to counter tube thinning due to the higher expansion, two end-feed actuators, each with 1112 kN (250 kip)
Table 2 Constitutive parameters of the Johnson–Cook model for the different tubular materials used. Material
t0 (mm)
a (MPa)
b (MPa)
n
c
m
DDQ HSLA-350 HSLA-350 DP-600 DP-780
1.8 1.5 1.8 1.8 1.5
211.6 453.0 453.0 350.0 584.0
516.7 617.5 617.5 655.7 831.0
0.300 0.615 0.615 0.189 0.348
0.0346 0.0255 0.0255 0.0144 0.0120
0.822 0.629 0.629 0.867 1.230
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1000
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1200 DP780 1.5mm
1360 s-1
True Stress (MPa)
True Stress (MPa)
800 DP600 1.8mm 600
HSLA 1.5mm HSLA 1.8mm
400
DDQ 1.8mm
200
120 s-1
910 s-1
38 s-1 0.1 s-1
440 s-1
0.003 s-1
900
600 0
0.02 0.04 0.06 0.08
0.1
0.12 0.14 0.16 0.18
0.2
Effective Plastic Strain (mm/mm) 0 0.00
0.05
0.10
0.15
0.20
0.25
0.30
True Strain Fig. 2. True stress vs. true strain for all materials used in the research. Figure shows tube material data in the 3 o’clock tube position.
force, are used to push on each end of the tube. End-feeding pushes material into the die, thereby increasing the formability of the tubes. Tubes formed using the low-pressure method are generally easy to manufacture, with very little or no failure or wrinkling problems occurring. The success of the high-pressure process, on the other hand, is highly dependent on a number of variables, including material formability, friction conditions, and most importantly, the loading paths (pressure and end-feeding) used to form the tube. The loading paths in the THF process are traditionally determined using trial and error procedures and often rely on past experience of the operator. The THF process is further complicated if new materials and die geometries are used for which the operator has no prior knowledge. The traditional process is both time-consuming and expensive. Furthermore, there is no guarantee that ‘‘optimum’’ pressure and end-feed profiles can be found by the trial and error process. Therefore, in order to determine the pressure and end-feed hydroforming profiles for any material and die geometry, an integrated approach to the problem comprised of the finite element analysis of the hydroforming process, a failure model, and an optimization code was used to hydroform the tubes successfully. Details about the process used to hydroform the tubes and the optimization method are given by Abedrabbo et. al [15].
Fig. 4. True stress vs. effective plastic strain for DP780 tube specimens (3 o’clock) at room temperature and strain rates from 0.003 s1 to 1360 s1.
3.2. Axial crush experiments Hydroformed and non-hydroformed tubes were crushed dynamically using a deceleration sled-track apparatus at the GM R&D Technical Center in Warren, Michigan. 3.2.1. Tube preparation All hydroformed tubes were trimmed such that the length of the square section of the tube prior to impact was 400 mm. The nonhydroformed tubes were cut to a length of 450 mm. In order to mount the tubes in the sled-track impact system, clamps were used on each end with solid bosses inside the clamping region of the tube to prevent the clamping force from crushing the tube at the clamping area. The bosses are essentially steel inserts manufactured to fit snugly inside the ends of the tube. For the non-hydroformed tubes, round bosses of 50 mm length each were used, while for the hydroformed tubes, bosses of 25 mm length each were used. In both the hydroformed and non-hydroformed cases, the impact length of the tube, i.e. contact free area, was 350 mm.
HP 40 LP 30 NH
1200
True Stress (MPa)
910 s-1
1360 s-1
120 s-1 38 s-1
0.1 s-1 440 s
800
0.003 s-1
-1
Tube Height (mm)
20 10 0 -10 -20 -30 -40 -40 400 0
0.02 0.04 0.06 0.08
0.1
0.12 0.14 0.16 0.18
0.2
Effective Plastic Strain (mm/mm) Fig. 3. True stress vs. effective plastic strain for DP780 sheet specimens at room temperature and strain rates from 0.003 s1 to 1360 s1.
-30
-20
-10
0
10
20
30
40
Tube Width (mm) Fig. 5. Comparison between the original round tube size (NH) and the low- and highpressure hydroforming processes for the 6 mm radius dies. The small square represents the final low-pressure (LP) tube, while the larger square represents the high-pressure (HP) process tube.
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Fig. 6. Experimental and numerical implementation of the crush initiators for one of the materials. (a) Side view of experimental implementation of initiators, (b) top view of numerical model, and (c) side view of numerical model showing initiator.
Crush initiators were formed into the impact end of the hydroformed tubes to reduce the initial impact force so as not to damage the load cells used in the impact tests. Also, the crush initiators assisted in the folding behaviour of the tube. No initiators were formed on the non-hydroformed tubes. The crush initiators were implemented on one side of the flat section of the tubes 50 mm from the top of the tube. The depth of each initiator ranged between 3.0 mm and 5.0 mm from the surface of the tube depending on material type. The different depths were used to avoid inducing cracks in the materials when making the indentations. Initiators were implemented in the numerical models in LSDYNA prior to the impact simulation. Initiators for each material were created with the specific depth that was recorded from the experimental phase. Adaptive meshing was also used in the numerical model to allow for finer elements in the initiator area. Fig. 6 shows a sample of one of the tubes showing the initiator and the numerical representation of the crush initiators. 3.2.2. Axial crush test procedure Impact testing of the round (non-hydroformed) tubes and of the tubes hydroformed using both the low- and high- pressure
processes was performed using a deceleration sled-track apparatus. Barrier impact testing uses a mule (sometimes termed a sled), with a structure attached to the front of the mule. This combination impacts a fixed barrier which is advantageous in that high speeds and large masses can be used. The deceleration sled used in this research has several advantages over the drop tower test. First, the mass of the sled can be much larger than the drop tower, which may be important when larger structures are tested. Second, the sled is constrained on a rail system which prevents rotation of the sled. Fig. 7 shows a schematic of the sled-track setup used to impact the axial tubes. The axial tubes were mounted on steel plates at both ends using the solid steel internal bosses and external clamps. The clamps were grooved on the clamping surface so as to minimize the slip of the tube over the bosses. In order to eliminate steel-on-steel impact, therefore minimizing the ringing in the system, a layer of plywood and rubber was placed on the impacted plate. The impact forces during the crash tests were measured using four 100 kN load cells placed at the base of each tube. To prevent the moving sled from damaging the load cells and hitting the fixed barrier when the tubes were fully crushed, stoppers covered with an aluminum
Moving Sled
Clamps & Bosses Hexcel Stopper
Load Cells
Right side (facing barrier)
Left side (facing barrier) Fixed Barrier
Fig. 7. Schematic of impact test setup for axial tubes.
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Fig. 8. Impact test result of (a) non-hydroformed, and (b) hydroformed tubes using the sled-track impact setup at GM R&D. The tubes are shown at the end of the impact test where the tubes folding (crushing) behaviour is shown.
honey-comb material (referred to as Hexcel) were mounted on both sides of the tubes to fully halt the motion of the sled. In all tests performed, the mass of the moving sled was 1145 kg. In the sledtrack setup, all tubes were impact tested using two tubes simultaneously, as shown in Fig. 7. Fig. 8 shows a sample result of the impact experiments for both the non-hydroformed (Fig. 6a) and hydroformed (Fig. 6b) tubes. The general folding behaviour of both types is evident in these photographs. The non-hydroformed tubes were impacted at a sled velocity ranging between 8.0 m/s and 9.0 m/s. The hydroformed tubes were impacted at a sled velocity between 7.0 m/s and 8.0 m/s. In the numerical analysis, the exact impact speeds from the experiments were used for each tube in order to replicate the test conditions accurately. 4. Numerical simulations 4.1. Hydroforming simulations The low-pressure hydroforming process was simulated using a lower die half, an upper die half, and the tube corresponding to the experimental setup. Both die halves were discretized using rigid shell elements of approximately 2.0 2.0 mm size with material properties of steel assigned for use in the contact treatment. The bottom die was constrained to be fixed and the top die was allowed to move in the vertical direction. The tube was meshed using approximately 2.0 2.0 mm Belytschko-Tsay [22] shell elements. The mesh geometries of both the tube and die halves used in the low-pressure process are shown in Fig. 9. Two die setups were created, one for each of the corner radius (6 mm and 18 mm) used in the research. The high-pressure simulations were created using a single die, representing the entire interior of the die surface, as opposed to the two halves used in the low-pressure simulations, due to the fact that the die in these experiments was always closed during the fluid pressurization process. Fig. 10 shows a cutaway view of the high-pressure hydroforming process showing the die, tube and both end-feed tools. As the fluid pressure increased, the end-feed tools are used to push more material into the die to compensate for material thinning. The end-feed displacement and internal tube pressure were applied numerically vs. time and matched the profiles used in experiments [15]. Engineering strains were measured from the formed tubes using the circle grid analysis technique [23] after the hydroforming
operations. These measured values were then compared to predicted strains from the simulations. All strain measurements were taken at the half-length of the tube around the circumference. Fig. 11 shows predicted and measured engineering strains for one of the DP600 1.8 mm tubes formed using the low-pressure process with the 6 mm corner radius die. Fig. 12 shows the results for one of the DP600 1.8 mm tubes formed using the high-pressure process with the 6 mm corner radius die. The engineering strains are plotted vs. angle around the tube, where the weld seam was at approximately 0 . Measurements were made for every other circle grid around the perimeter of the tube. As seen from these two figures, the numerical models predicted the strain results well. Fig. 13 shows the predicted thickness distribution around the perimeter of the tube for four sample tubes hydroformed using the low- and high- pressure hydroforming processes with both the 6 mm and 18 mm corner radius dies (R6 and R18). The results shown are for sample DP600 1.8 mm hydroformed tubes. As seen from the graph, the high-pressure hydroforming process caused a high level of tube thinning when compared to the low-pressure process. In the high-pressure cases, the maximum percentage change in tube thickness due to hydroforming, from a nominal tube thickness of 1.8 mm, was 11.5% for the 6 mm die corner radius case and 10.5% for the 18 mm die corner radius case, compared to only 2.8–3.3%, respectively, for the low-pressure cases. Experimental verification of the tube thickness results was carried out using an ultrasonic measurement device which measured the thickness changes after hydroforming. The thickness measurements, however, were performed only on the high-pressure tubes. The
Top Die (2x2 mm mesh)
Bottom Die (2x2 mm mesh) Tube (2x2 mm mesh) Fig. 9. Low-pressure LS-DYNA simulation model of the low-pressure hydroforming process.
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next. Also, between each forming step, a springback simulation was performed on the tube. The forming steps performed on each of the tubes in the numerical analysis are as follows:
Tube
Die
1. 2. 3. 4. 5.
Hydroforming process (low- or high- pressure); First springback; Crush initiator forming; Second springback; Trimming of the tube to the impact length, checking of element quality and adjusting if necessary; and 6. Impact simulation.
End Feed Tools
Fig. 14 shows a schematic of the various forming processes performed on the tube from the initial stock state to the final impact procedure.
Fig. 10. Cutaway view of the high-pressure hydroforming simulation process.
5. Axial crush experimental and numerical results thicknesses changes in the low-pressure cases were very small and thus difficult to measure using the ultrasonic device (measurements fall within the noise of the device). The measured results for the high-pressure process closely matched the predicted results. 4.2. Axial crush simulations A rigid wall was used to simulate the sled-track platform in the finite element simulations of the impact tests. The mass and impact velocity specified for the rigid wall corresponded to the experimental values for each simulated test. A second rigid wall was used at the bottom of the tube to prevent it from deforming past the bottom plane during the simulation. All nodes along the bottom edge of the tube were fully constrained. The rotational degrees of freedom were constrained for the nodes along the top edge of the tube in order to prevent unrealistic deformation modes [24]. A numerical parametric study on the effects of including the masses of the bosses and the clamps used in the experiments showed that their effect is minimal, due to the fact that the bosses and clamps were stationary prior to impact. Consequently, the geometry and masses of the bosses and the support clamps were not taken into account in the current simulations. In order to include the forming history data in the impact tests, the tube thickness, residual strains, residual stresses and work hardening from each simulation process performed on the tube prior to the impact step was carried forward from one step to the
In total, there were five non-hydroformed, 10 low-pressure and 10 high-pressure numerical simulations performed in this research. In the experiments, at least four tubes were crushed for each corresponding numerical simulation for a total of 100 tubes. An additional number of setup impact tests were performed for each material to better understand the required impact speeds. The results of the crush tests are mainly presented based on crush force vs. crush distance from which the energy absorption and mean crush loads can be determined. Due to the mechanics of the impact tests, a noticeable level of noise was present in the measured force data. In order to reduce the amount of noise generated by the impact, a mechanical Butterworth filter was installed with the load cells. For the numerical simulations, a similar Butterworth filter was applied to the impact forces in order to match the experimental tests. The experimental and numerical filters each used a 1.0-kHz filter frequency. All force measurements presented in this research, experimental and numerical, had the Butterworth filter applied to them. The energy absorption and mean crush load can be determined from the crush data based on the following equations:
EðxÞ ¼
Z
w
FðxÞdx
(5)
0
Pm ¼
EðwÞ w
(6)
25 Max Strain - Exp Max Strain - Num
Major Engineering Strain (%)
20 15 10 5 0 -5 -10
0
45
90
135
180
225
270
315
360
Angle (Degrees) Fig. 11. Predicted and measured engineering strains for DP600 1.8 mm tube formed using the low-pressure hydroforming process with the 6 mm corner radius die.
N. Abedrabbo et al. / International Journal of Impact Engineering 36 (2009) 1044–1057
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40 Max Strain - Exp Max Strain - Num
Major Engineering Strain (%)
35
HP
30 25 20 15 10 5 0
0
45
90
135
180
225
270
315
360
Angle (Degrees) Fig. 12. Predicted and measured engineering strains for DP600 1.8 mm tube formed using the high-pressure hydroforming process with the 6 mm corner radius die.
where E(x) is the energy absorption, F(x) is the crush force, w is the crush distance up to which the energy absorption is taken, and Pm is the mean crush load. Fig. 15 shows a typical plot of the predicted and measured crush load and mean crush load vs. crush distance. The figure shows the results for the non-hydroformed HSLA-350 1.8 mm tubes. Fig. 16 shows the predicted and measured crush load and mean crush load vs. crush distance for the HSLA-350 1.8 mm tubes formed using the low-pressure hydroforming process with the 6 mm corner radius die. Fig. 17 shows the corresponding results for the HSLA-350 1.8 mm tubes formed using the high-pressure hydroforming process with the 6 mm corner radius die. A numerical model that accurately predicts the internal energy compared to experiments is a good indication that the numerical constitutive models used in the simulations are sufficiently accurate. The total energy absorption and mean crush loads were calculated up to 200 mm crush distance for all crush responses obtained.
In the experiments, it was noticed that in some cases the start of the data acquisition from the sled-track did not always correspond to a crush distance of zero. In such cases, the start of the crush distance was adjusted to be zero when the crush load was greater than 1.0 kN. The general folding behaviour for the non-hydroformed tubes in the impact tests varied between diamond mode, non-axisymmetric, and mixed mode (both diamond and non-axisymmetric mode). Fig. 18 shows a sample comparison between the observed and predicted crush modes for DDQ 1.8 mm non-hydroformed tubes impacted at a speed of 7.93 m/s. In general, the numerical simulations accurately captured the crush mode of the nonhydroformed tubes. The general folding behaviour for the hydroformed tubes in the impact tests was symmetric. Fig. 19 shows a comparison between the observed and predicted crush modes for DP600 1.8 mm tubes hydroformed using the low-pressure process with a die corner
1.95 Nominal Thickness Low Pressure - R6 Low Pressure - R18 High Pressure - R6 High Pressure - R18
Tube Wall Thickness (mm)
1.90 1.85 1.80 1.75 1.70 1.65 1.60
0
45
90
135
180
225
270
315
360
Angle (Degrees) Fig. 13. Predicted tube thickness distribution around the perimeter for DP600 1.8 mm tubes hydroformed using the low- and high- pressure processes formed with the 6 mm and 18 mm corner radius dies (R6 & R18). Data taken at half-length of the tube.
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Fig. 14. A schematic of the steps performed on the each tube from stock to impact.
radius of 6 mm and impacted at a speed of 7.74 m/s. The final length of the tube in the experiments was 179.6 mm, while, in the numerical simulation, the final length of the tube was 179.8 mm. In general, the simulations accurately captured the crush mode of the hydroformed tubes. In all of the simulations performed in this research, the accuracy of the numerical results relative to the experimental values was 3.0–7.0% for the low-pressure hydroforming process and 1.0–8.0% for the high-pressure hydroforming process. These results indicate that the numerical procedures and the developed constitutive models used in both the hydroforming and impact numerical analysis were capable of predicting the experimental test results accurately.
the mean crush loads were plotted as a function of the corner radius of the various dies. Fig. 20 shows a plot of the predicted mean crush loads vs. corner radius ratio for the tubes hydroformed with the low-pressure process. In this figure, corner radius ratio is taken as the ratio of the as-formed corner radius (6 mm or 18 mm) to the initial tube radius (38.1 mm). A corner radius ratio of unity represents the non-hydroformed tubes. As seen from Fig. 20, the hydroformed tubes show a decrease in energy absorption with decreasing corner radius ratio. This reduction is attributed both to the change in the shape of the tube from round to square (and corresponding change in crush mode) and to the thinning of the tubes, especially at the corner regions, caused by the circumferential expansion during the hydroforming process.
5.1. Axial crush results of the low-pressure hydroformed tubes
5.2. Axial crush results of the high-pressure hydroformed tubes
In order to study the effects of the hydroforming process and initial geometry on the impact characteristics of the different tubes,
Fig. 21 shows a plot of the predicted mean crush loads vs. corner radius ratio for tubes formed using the high-pressure hydroforming
300 250
Crush Load (kN)
b
Numerical Experimental #1 Experimental #2
Mean Crush Load (kN)
a
200 150 100 50 0
200
Numerical Experimental #1 Experimental #2
150
100
50
0 0
50
100
150
Crush Distance (mm)
200
0
50
100
150
200
Crush Distance (mm)
Fig. 15. Crush response for non-hydroformed HSLA-350 1.8 mm tubes. (a) Crush force vs. crush distance. (b) Mean crush load vs. crush distance.
Crush Load (kN)
a
250 Numerical Experimental #1 Experimental #2
200 150 100 50
b
120
Mean Crush Load (kN)
N. Abedrabbo et al. / International Journal of Impact Engineering 36 (2009) 1044–1057
100
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Numerical Experimental #1 Experimental #2
80 60 40 20 0
0 0
50
100
150
0
200
Crush Distance (mm)
50
100
150
200
Crush Distance (mm)
Fig. 16. Crush response for HSLA-350 1.8 mm tubes formed using the low-pressure hydroforming process with the 6 mm corner radius die. (a) Crush force vs. crush distance. (b) Mean crush load vs. crush distance.
5.3. Low- vs. high- pressure hydroformed tubes Table 3 shows a comparison of the measured absorbed energy for all of the tubes impact tested in this research. Results shown are for tubes hydroformed with the low-pressure (LP) and high-pressure (HP) processes; both formed using the two types of dies (6 mm and 18 mm). The mean crush results of the non-hydroformed tubes are also shown in the table. From the results shown in Figs. 20 and 21 and Table 3 it is clear that for all materials, the current low-pressure process offers better energy absorption characteristics than the high-pressure hydroforming process. This finding is attributed in part to the fact that the cross sectional thickness of the high-pressure tubes is less than the low-pressure tubes (see Fig. 13), which is a direct consequence of the high-pressure process causing larger expansion in the tubes than the low-pressure process [15]. The difference between the two processes is especially apparent for the 18 mm corner radius die.
Crush Load (kN)
a
250
Numerical Experimental #1 Experimental #2
200 150 100 50
6. Constitutive model effects of numerical analysis accuracy In this research, material characterization was performed on all materials in both the sheet form and the as-formed tube form. From these tensile tests, the parameters of two constitutive models (flow stress models), the Power-Law model and the Johnson–Cook model, were fit to the experimental results for each material. During the various forming processes performed on the tube from the initial stock state to the final forming step prior to impact (see Fig. 14), strain rate effects are very minimal. Therefore, for these simulations, the Power-Law model was used in the numerical analysis. In the impact part of the experiments, however, strain rates vary over a large range. Also, due to heat from plastic deformation, the adiabatic temperature increases in the material, resulting in material softening. For these reasons, the Johnson– Cook model, which incorporates these two effects, was used in the numerical analysis of impact. In order to highlight the significance of performing detailed material characterization and the use of the correct constitutive model in numerical analysis, two simulations were performed. In the first one, the impact part of the analysis was performed using the Johnson–Cook model (which includes strain rate effects). In the second part, the impact analysis was performed using the PowerLaw model (which does not include strain rate effects). These two simulations also demonstrate the strain rate effects on the impact results. Fig. 22 shows the mean crush load results for the HSLA-350 1.8 mm tube formed using the low-pressure hydroforming process with 6 mm corner radius die. The figure shows the actual measured
b
140
Mean Crush Load (kN)
process. Again, a corner radius ratio of unity represents the nonhydroformed tubes. As evident in Fig. 21, the tubes hydroformed with the highpressure process show a similar decrease in energy absorption with decreasing corner radius ratio. This reduction is also attributed both to the change in the shape of the tube from round to square and to the thinning of the tubes caused by the circumferential expansion during the hydroforming process. The reduction in tube thickness has a direct influence on the energy absorption characteristics during crash.
120
Numerical Experimental #1 Experimental #2
100 80 60 40 20 0
0 0
50
100
150
Crush Distance (mm)
200
0
50
100
150
200
Crush Distance (mm)
Fig. 17. Crush response for HSLA-350 1.8 mm tubes formed using the high-pressure hydroforming process with the 6 mm corner radius die. (a) Crush force vs. crush distance. (b) Mean crush load vs. crush distance.
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140 DP600 1.8mm
Mean Crush Load (kN)
120
DP780 1.5mm
100
HSLA 1.8mm DDQ 1.8mm
80
HSLA 1.5mm
60 40 20
0.2
NH
R18
R6 0 0.0
0.4
0.6
0.8
1.0
1.2
Corner Radius Ratio Fig. 20. Predicted mean crush loads vs. corner radius ratio for the monolithic tubes formed with the low-pressure process. A corner ratio of 1.0 represents the nonhydroformed tube.
Fig. 18. Observed and predicted crush modes for impact test of a non-hydroformed tube showing the general folding behaviour seen in the round tubes. Result shown is for the DDQ 1.8 mm non-hydroformed tube.
Power-Law model (with no strain rate effects) lowered the accuracy of the predicted results by approximately 27% compared to the actual experimental results. Using the Johnson–Cook model (with strain rate effects included) improved the accuracy dramatically. These results also demonstrate the importance of using the correct constitutive model in numerical analysis if accurate results, compared to experiments, are to be achieved. 7. Forming history effects on numerical analysis accuracy
experimental results, the predicted numerical results using the Johnson–Cook model (strain rate effects included), and the predicted numerical results using the Power-Law model (no strain rate effects). As seen from Fig. 22, strain rate effects are important during the impact part of crash simulations of these materials. Using the
The hydroforming and impact numerical results presented earlier were performed using the ‘‘carry forward’’ procedure. In this numerical scheme, the forming history data, i.e. residual stress, residual strain, work hardening (effective plastic strains), and material thickness changes, from each simulation step performed on the tube, e.g. hydroforming, trimming, etc., were used as input for the next step in the simulation process. This procedure was employed in order to ensure the accuracy of the numerical analysis and it has been confirmed by the good agreement between the numerical predictions of the impact tests and the measured impact data. A parametric study was performed to assess the importance of transferring the forming history between the numerical
140
Mean Crush Force (kN)
DP600 1.8mm
120 DP780 1.5mm
100
HSLA 1.8mm DDQ 1.8mm
80
HSLA 1.5mm
60 40 20 R6 0 0.0
0.2
NH
R18 0.4
0.6
0.8
1.0
1.2
Corner Radius Ratio Fig. 19. Observed and predicted crush modes for impact test of a square hydroformed tube showing the general symmetric folding behaviour found in the hydroformed tubes. Result shown is for DP600 1.8 mm tube hydroformed with the low-pressure process with the 6 mm corner radius die.
Fig. 21. Predicted mean crush loads vs. corner radius ratio for the monolithic tubes formed using the high-pressure process. A corner ratio of 1.0 represents the nonhydroformed tube.
N. Abedrabbo et al. / International Journal of Impact Engineering 36 (2009) 1044–1057 Table 3 Experimental absorbed energy results for the low-pressure (LP), high-pressure (HP) and the non-hydroformed (NH) tubes. t0 (mm)
Material
Die corner radius 6 mm
DDQ HSLA-350 HSLA-350 DP600 DP780
1.8 1.5 1.8 1.8 1.5
18 mm
38.1 mm
LP (kJ)
HP (kJ)
LP (kJ)
HP (kJ)
NH (kJ)
10.2 8.3 12.0 14.3 11.5
9.7 8.1 10.5 13.9 11.3
12.2 9.7 13.2 15.9 15.7
10.2 9.0 11.2 13.7 12.5
17.3 16.4 18.0 22.4 21.4
Table 4 Forming history effects for the low-pressure process showing predicted absorbed energy and predicted peak load for multiple cases and percentage change of each case from the full history case. Case #
Forming history case
Absorbed energy at 200 mm (kJ)
(1) (2) (3)
Full forming history Sheet data No residual stress or work hardening No thickness change No forming history
11.13 10.48 10.27
(4) (5)
simulations of the multiple forming operations performed on the tubes. The following parametric studies considered the HSLA-350 1.8 mm tubes formed using both the low- and high- pressure hydroforming processes: 1. Full forming history: in this case, all forming history data were transferred between the simulations (the default case for the data presented thus far). This case is used for comparison purposes with the other cases. 2. Sheet data material properties: in these simulations, the asreceived sheet data, rather than stress–strain data acquired from tube samples, were used for all numerical simulations performed on the tube. All forming history data in this case were carried forward between the simulations. The impact simulations utilized a Johnson–Cook model but with constants derived from high rate testing of sheet samples. This case was used to assess work hardening effects on the material properties as a consequence of the roll-forming operation used to manufacture the tubes from sheet material. 3. No residual stress or work hardening: in these simulations, both residual stress and work hardening (effective plastic strains) were not transferred between the forming steps performed on the tube. All other forming history data, in particular thickness change, were included. In this analysis, tube material data were used for all simulations. 4. No thickness change: in this analysis, element thickness changes due to material deformation were suppressed for all forming steps performed on the tube. All other forming history data (residual stress, work hardening) were included. Tube material data were used.
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% Change
Peak load (kN)
% Change
0.00 5.84 7.73
117.27 108.15 101.25
0.00 7.78 13.66
10.75
3.41
113.31
3.38
9.95
10.60
98.15
16.30
5. No forming history: in this analysis, no forming history data, i.e. residual stress, work hardening (effective plastic strains), and material thickness changes, were transferred between the different steps. Tube material data were used in this part of the analysis. NOTE: a parametric study was also performed where no residual strain data were transferred between the forming steps performed on the tube. The results showed, however, that the effects of not transferring the residual strain between the different steps were between 0.02% and 0.04%, which is negligible compared to the other cases (see Tables 4 and 5). Next, the results of the parametric study will be presented followed by analysis of these results. 7.1. Comparative study results Fig. 23 shows the predicted mean crush load for the parametric cases for low-pressure hydroforming of HSLA-350 1.8 mm tube using the 6 mm corner radius die. Fig. 24 shows the corresponding results for the high-pressure process using the same material and corner radius die. Results for the case when full forming history data were included in the analysis are also shown for comparison purposes. In Table 4, results of both the predicted absorbed energy at a crush distance of 200 mm and the predicted peak load are presented for all the parametric cases of the low-pressure process. The percentage change of each case from the full history case is also given. Table 5 shows the corresponding results for the high-pressure process with percentage change from the full history case. 7.2. Analysis of comparative study
120 Experimental Numerical - Johnson-Cook model Numerical - Power-Law model
Crush Load (kN)
100
80
60
From the results of the comparative study, the effects of not transferring the forming history data between the various numerical simulations performed on the tube are apparent. For the lowpressure hydroforming process, the case with the lowest effect on the results is the one where no thickness changes are transferred (3.41%). The highest effect was the case when no forming history data were included (11–16%). Table 5 Forming history effects for the high-pressure process showing predicted absorbed energy and predicted peak load for multiple cases and percentage change of each case from the full history case.
40
20
0 0
50
100
150
200
Crush Distance (mm) Fig. 22. Mean crush load vs. crush distance for HSLA-350 1.8 mm tube formed using the low-pressure hydroforming process with 6 mm corner radius.
Case #
Forming history case
Absorbed energy at 200 mm (kJ)
% Change
Peak load (kN)
% Change
(1) (2) (3)
Full forming history Sheet data No residual stress or work hardening No thickness change No forming history
10.80 10.10 8.140
0.00 6.48 24.63
148.31 144.13 113.31
0.00 2.82 23.60
13.32
þ23.33
180.67
þ21.82
9.40
12.96
131.89
11.07
(4) (5)
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120
(1) Full Forming History (2) Sheet Data (3) No R. Stress or Work Hardening (4) NoThickness Change (5) No Forming History
Mean Crush Load (kN)
100
80 Full Forming History Case 60
40
No Forming History Case
20
0
0
50
100
150
200
Crush Distance (mm) Fig. 23. Forming history effects for the HSLA-350 1.8 mm tube showing mean crush load results for the low-pressure hydroforming process with the 6 mm corner radius.
For the high-pressure case (where tube thinning is higher than the low-pressure case) the effects of forming history data are more apparent. For the case where no thickness changes were transferred, the peak load and energy absorption of the tube increased by approximately 22% and 23%, respectively. This finding was due to the fact that since no thickness changes occurred during the forming process, the cross sectional thickness of the tube was higher; which translates into higher energy absorption. When residual stress and work hardening effects are not transferred, the results are highly affected, reducing the energy absorption capability by approximately 23%. It should be noted that although the ‘‘no forming history’’ case in the high-pressure results appears to have a lesser impact on the accuracy than the ‘‘no thickness change’’ and the ‘‘no residual stress and work hardening’’ case, this finding is misleading. In the ‘‘no forming history’’ case, while not including the residual stress and work hardening lowers the energy absorption characteristics, the increased tube thickness (due to no thickness change effects) increases it, and, therefore, these two counteract each others effect. In both the low- and high- pressure forming cases, using the sheet data in the simulations instead of the tube data lowered the accuracy of the results between 3% and 8%. This result
150
Mean Crush Load (kN)
demonstrates the effect of work hardening due to the operations of manufacturing the tube from sheet material. Also, it demonstrates the importance of performing material characterization on the tube material and using those results in any numerical analysis rather than sheet data.
(1) Full Forming History (2) Sheet Data (3) No R. Stress or Work Hardening (4) No Thickness Change (5) No Forming History
100
50
0 0
50
100
150
200
Crush Distance (mm) Fig. 24. Forming history effects for the HSLA-350 1.8 mm tube showing mean crush load results for the high-pressure hydroforming process with the 6 mm corner radius.
8. Conclusions and recommendations In this research, the crash performance of hydroformed and non-hydroformed steel tubes of varying strength levels was investigated. Tubes were hydroformed using both the low- and high- pressure hydroforming processes. Material characterization of the different materials was carried out using several methods. From these tests, the constitutive model parameters for both the Power-Law and Johnson–Cook models were determined for all tube materials to be used in the finite element analysis. Tube crash testing was performed on both the non-hydroformed and hydroformed tubes using a sled-track impact system and several data, including force and energy, were also collected. From the extensive experimental and numerical analyses performed on the different tubes in this research, the following conclusions and recommendations are made: 1. Analysis of the collected data (measured and predicted) showed that the AHSS materials offered the highest energy absorption in a crash event. The dual phase (DP) materials resulted in the highest energy absorption. 2. One of the important factors affecting energy absorption during impact was thickness reduction caused by circumferential expansion of the tubes during the hydroforming process. The energy absorption capabilities of the tubes decreased as the radius ratio (corner radius/initial radius) decreased – a direct result of decreased wall thickness. 3. The results also indicated that tubes formed using the lowpressure process have higher energy absorption capabilities than the tubes formed with the high-pressure process. Again, this can be attributed to the fact that the tube thickness changes caused by each forming process are different, where the high-pressure tubes have higher thickness reduction than the low-pressure tubes (see Fig. 13). 4. Material characterization is very important in order to extract accurate constitutive model parameters for the different materials to be used in numerical analysis. 5. Using the as-formed material characterization data, as opposed to using only sheet material data, improves the accuracy of the numerical analysis by 5–7%. 6. In order to obtain accurate simulation results, it is critical to use the correct constitutive equation (flow rule) to represent the material in numerical analysis. In the impact part of the simulations, strain rates vary over a large range and the adiabatic temperature increases in the material due to heat from plastic deformation. Therefore, for the impact part of the analysis, the Johnson–Cook model was used to capture that material behaviour. Using the Power-Law model (which does not include strain rate effects) to represent the material during the impact simulations produced an error of 27% as compared to the Johnson–Cook model and experimental results. 7. The effect of forming history on the accuracy of the numerical results was clearly demonstrated. Failing to transfer one or all of the forming history parameters between the different numerical simulations produced large errors in the numerical results. 8. Finally, the accuracy of the numerical methods and constitutive parameters developed in this research offers a very attractive tool to engineers and designers. With little experimental verification, these numerical models can be used to better
N. Abedrabbo et al. / International Journal of Impact Engineering 36 (2009) 1044–1057
understand and perform extensive analytical studies on the performance of the advanced high-strength steels.
Acknowledgments Financial support for this research from General Motors of Canada Limited, Dofasco, the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Research and Development Challenge Fund is gratefully acknowledged.
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