Effects of Mechanical Properties of Steels on Dynamic Collapse Behavior of High Strength Steel Hat Columns

Abstract

We investigated the relationship between the material properties and axial collapse behavior of hat-section hollow columns made of high-strength steels. Dynamic collapse tests of the columns and FEM simulations were conducted using high-strength steels with various tensile strengths and n-values. Materials that exhibited yield point elongation (YPEl) underwent enhanced accordion-type deformation in axial collapse owing to the occurrence of long wave buckling on the hat walls in the early stage of collapse. In addition, it was important to avoid fracture in the initial buckling region to induce progressive crumpling behavior. A high n-value of the material was favorable for avoiding fracture by increasing the bend radii and decreasing the strain concentration at the buckling regions on the hat walls, thereby resulting in stable progression of accordion-type folds. In conclusion, steels exhibiting YPEl and high n-values are favorable for inducing stable accordion-type deformation during axial collapse.

 

This Paper was Originally Published in Japanese in J. JSTP 60 (2019) 123–129.

1. Introduction

In recent years, improving the fuel efficiency of automobiles has become an important issue due to the demand for reduced greenhouse gas emissions, and there has been active utilization of ultra-high strength steels aimed at reducing the weight of automobile bodies by decreasing the thickness of their parts.^1,2) The role of the passengers’ cabin—which forms part of the automobile body—is to maintain shape when a collision occurs, thereby securing a space in which the passengers can survive. For this reason, there has been an increase in the strength of the materials used in the cabin. Currently, hot stamped steel sheets³⁾ with an ultimate tensile strength (UTS) of 1500 MPa are widely utilized. In contrast, the role of the frame parts at the front and rear sections of the body structure is to absorb impact energy by deforming during collision. Frame parts mainly utilize high strength steels of class 590 MPa or 780 MPa, and, with a few exceptions,⁴⁾ the use of still stronger materials is yet to be achieved.

This is because, in the case of frame parts, higher strength may not bring commensurate improvements in performance, mainly due to two factors. The first is the occurrence of fracture due to poor ductility associated with the increase in strength. Since the front and rear frames undergo a large amount of deformation during collision, the fracture of the material leads to loss of crash energy absorption and variations in performance. One way of dealing with this problem is to improve the deformability of the material.⁴⁾ The second factor is the instability of the deformed shape. Generally, frame parts undergo “axial collapse” in which they are deformed along their longitudinal direction under the impact load.^5–8) In this case, the hollow column part can absorb a large amount of crash energy by deforming into an “accordion shape” in which a sequence of folds are formed. However, previous studies have shown that columns made of materials of class 980 MPa or stronger are not easily deformed into this accordion shape, resulting in loss of efficiency of crash energy absorption.^9–11) Since shape factors have a large effect on the stability of axial collapse,⁷⁾ the addition of crush beads to act as the starting point for buckling, and the adoption of a regular polygonal column section to enable stable collapse,¹²⁾ etc. have been investigated as measures to deal with this problem. In addition, it is also important to improve the stability of axial collapse from the viewpoint of material properties if these measures are difficult to implement due to design constraints. For example, finite element method (FEM) simulations have shown the possibility of enabling collapse to a stable accordion shape by increasing the work hardening capability of the material.^8–10) As an example of ultra-high strength steel with high work hardening capability, Okitsu et al.^10,11) used an ultrafine-grained multi-phase steel in an axial collapse test, and demonstrated that stable continuous accordion-shaped deformation was readily obtained. In these studies,^10,11) the relationship between the work hardening rate (n-value) of the material and shape of the crushed column was considered, but many points remain unclear. For example, the critical n-value for achieving a stable accordion shape, and the effects of other material properties such as UTS and bendability have not been clarified.

Therefore in this study, hollow columns with hat cross-sections were fabricated using various ultra-high strength steel sheets with different n-values, UTS, bendability, and stress–strain curves (s–s curves), and these were used to conduct high-speed axial collapse tests in an attempt to clarify the effect of material properties on axial collapse stability.

2. Experimental Procedure

2.1 Axial collapse test

(1) Specimen materials

Two levels of UTS were used (classes 1180 MPa and 980 MPa), and four types of steel sheets of thickness 1.2 mm with different material properties were selected. Table 1 lists the YS (yield strength), UTS, YPEl (yield point elongation), u-El (uniform elongation), t-El (total elongation), and n-value of the materials used, and Fig. 1 shows nominal s–s curves obtained in quasi-static tensile tests. The tensile properties were measured at a strain rate of 3 × 10⁻³ s⁻¹ using JIS No. 5 test pieces with the tensile direction parallel to the rolling direction of the material. Steel A is a material that was shown to have a stabilizing effect on deformation during axial collapse in a previous study,¹⁰⁾ and has a fine multi-phase microstructure composed of ferrite, martensite and retained austenite. The UTS of steel A is class 1180 MPa, and it is characterized by a YPEl value of approx. 4.7% and subsequent high work hardening. Its n-value (which represents the work hardening capability of the material) is 0.33, which is higher than that of the other materials used. Note that the n-values of steels A and D were calculated in the strain range after YPEl. Steels B and C have dual phase (DP) microstructures composed of ferrite and martensite. Their respective UTS classes are 1180 MPa and 980 MPa, and they have s–s curves—characterized by continuous yield—that are typical of ferrite and martensite DP steels. However, their n-values are lower than that of steel A. Steel D was obtained by annealing steel B at 450°C for 10 min, and has a dual phase microstructure in which the martensite in steel B has been annealed into tempered martensite. Steel D has a UTS of class 980 MPa, and exhibits a YPEl value of approx. 2.5%, but has a lower n-value than steel C, which has the same level of UTS.

Table 1 Mechanical properties of the steels used in axial collapse tests.

Fig. 1

Nominal stress–strain curves of the steels used in axial collapse tests at a strain rate of 3 × 10⁻³ s⁻¹.

The dynamic tensile properties of the materials were also evaluated. Tensile specimens of gauge length 8 mm and width 2 mm, for which the tensile direction was parallel to the rolling direction of the material, were deformed at a strain rate of 10² s⁻¹ using a TS-2000 “load-sensing block type” servo-hydraulic material test system manufactured by Saginomiya.¹³⁾ Figure 2 shows the nominal s–s curves that were obtained. Due to the difference in shape of the parallel section of the specimens, the shape of the s–s curves after uniform elongation are different for high-speed and quasi-static deformation, but both exhibit the same kind of differences between materials with respect to yield behavior and work hardening characteristics.

Fig. 2

Nominal stress–strain curves of the steels used in axial collapse tests at a strain rate of 100 s⁻¹.

Bendability was also confirmed in accordance with JIS Z2248 (2006), using rectangular specimens for which the longitudinal direction was perpendicular to the rolling direction. Three-point bending was performed up to a bending angle of 180 degrees using punches of different radii. The minimum punch radius at which no cracks are visually observed was defined as the critical bending radius. Table 1 show R/t, which represents bendability and is given by the critical bending radius R divided by thickness t. Arranging the steel types in order of superior bendability gives the order D, C, B, A.

(2) Axial collapse test method

A 230 mm long hollow column specimen was used, which was composed of a hat section part and back plate, as shown in Fig. 3. The hat section part had the cross section shown in Fig. 3(a), and was prepared by 90 degree V-bending using a bending die with a punch radius of 5 mm. The hat section part and flat back plate were made of the same material, and were spot-welded at 5 points on the flanges of the hat section part at a pitch of 40 mm, forming the hollow column shown in Fig. 3(b). The column used in this study was given a flat rectangular cross section, which is less stable during axial collapse,⁷⁾ in order to help clarifying the difference in collapse stability between differing materials. The upper and lower ends of the columns were arc-welded to steel plates. Some of the column specimens were heat treated at 170°C for 20 min before the collapse test was performed in order to simulate the baking process after painting of the automobile body. Henceforth, this will be referred to as BH (bake hardening) treatment. The column specimens were axially deformed along the longitudinal direction using a free-fall type high-speed collapse test machine under the conditions shown in Fig. 3(c). Adopting conditions under which almost the entire length of the column was deformed, five to ten tests were performed on each type of steel with and without BH treatment and at different impact velocities. In addition, some columns were subjected to high-speed collapse tests in which the deformation was set to approx. 50 mm using a stopper, and to quasi-static compression using a hydraulic compression test machine with a cross-head speed of 50 mm·min⁻¹.

Fig. 3

Overview of the axial collapse experiment: (a) cross section, (b) appearance of the hat column, and (c) test conditions.

2.2 Bending test simulating the accordion type deformation region during axial collapse

The shape of the accordion type folds in the deformed hollow column can be expressed by repeating a unit called the “basic collapse element (BCE)”.^14,15) In this study, an attempt was made to reproduce the BCE from flat sheets in order to evaluate the effect of material properties on the shape of the buckled region during axial collapse.

(1) Specimen materials

Two kinds of steel sheets of thickness 1.0 mm were used. Table 2 shows their tensile properties in the direction perpendicular to the rolling direction. Steel E gives steel sheet equivalent to that of A, and exhibits YPEl and a high n-value. Steel F has a UTS of class 1180 MPa, consists of a martensitic structure with a small amount of ferrite, and has a lower n-value than steel E.

Table 2 Mechanical properties of the steels used in bending tests simulating basic collapse element.

(2) Bending test

Figure 4(a)–(c) shows the bending process used to fabricate the test specimens. First, a flat plate was bent to 100 degrees using a punch of radius 5 mm. After rotating the specimen by 90 degrees, the left and right planes created by the first bend line were each bent in opposite directions, as shown in Figs. 4(b) and (c). Figure 4(d) shows the BCE specimen after the bending process has been performed. The dotted lines a, b, and c correspond to the bends formed in Figs. 4(a), (b), and (c), respectively. Following this, the BCE specimen was folded in a compression testing machine as shown in Fig. 4(d), until fracture occurred. Fracture was judged by detecting the sound emitted by cracking at the specimen surface. Figure 4(e) shows an example of a column deformed axially in accordion shape, which is simulated by the BCE specimen.

Fig. 4

Outline of the bending test simulating the basic collapse element (BCE): (a)∼(c) Forming process, (d) appearance of the BCE specimen, and (e) appearance of a hat column deformed in an accordion shape.

3. Numerical Simulation

3.1 FEM simulation of axial collapse

Steel A, which has shown accordion type deformation in past studies,^10,11) is characterized by a large amount of YPEl, as shown in Fig. 1, which possibly affects axial collapse performance. Virtual s–s curves with different amounts of YPEl were therefore created, and deformation behavior was evaluated using FEM simulation.

A hat column model with the same shape and dimensions as in Fig. 3 was created using shell elements, and the spot-weld joints were represented by connecting opposite nodes on the hat section part and back plate with rigid elements. The elements at the lower end of the column were completely fixed, and those at the upper end were allowed to move only in the direction parallel to the longitudinal direction of the column. An initial velocity of 50 km·h⁻¹ was applied to the nodes at the upper end. A dynamic explicit analysis code, LS-DYNA, was used for analysis. As shown in Fig. 5, the analysis was performed using a material property that models the s–s curve of steel A and for which YPEl is 4%, and other material properties for which YPEl is 0% or 2% and for which the flow stresses in the high strain range are almost equal to those for steel A.

Fig. 5

Stress–strain data of the materials used in the FEM simulation of axial collapse.

3.2 FEM simulation of bending deformation

In the U-bending test for evaluating the bendability of materials and the bending test simulating the accordion type deformation region (BCE), punches of specific radii were used. Strictly speaking, the bending mode in these experiments is different from that during the actual axial collapse of hollow columns. In axial collapse, the initial flat surface of the column is compressed by the surroundings, causing out-of-plane buckling, and it undergoes “free” bending without being constrained by the bending radius of the punch. Henceforth, this behavior will be referred to as “free bending”.

FEM simulations were conducted to evaluate the behavior of each material during “free bending” deformation. Figure 6 shows the analysis model. The specimen was a 1.2-mm thick rectangular steel sheet of dimensions 40 mm × 25 mm, divided into 2-mm square shell elements. Both sides of the specimen were placed in contact with a rigid wall, and an initial velocity of 400 mm·s⁻¹ (1.4 km·h⁻¹) was applied to the right hand side wall. The elements at the left end of the specimen were only allowed to rotate around the contact points with the rigid wall. The elements at the right end were allowed to rotate freely, and to move parallel to the direction of motion of the rigid wall. An initial deflection of radius 2000 mm and displacement 0.1 mm was applied so as to deform the central area of the specimen. The analysis was performed using the dynamic explicit code RADIOSS. The s–s curves of steels A and B, shown in Fig. 1, were used as the material properties.

Fig. 6

FEM model for the “free–bending” simulation.

4. Results and Discussion

4.1 Axial collapse test

Figure 7 shows typical examples of the progression of collapse recorded with a high-speed video camera, and the final shapes of columns made of steels A, B, and C. For steel A, the first fold was generated near the upper end and then further folds were successively formed in the adjacent region, resulting in a stable accordion shape. This shape is considered ideal during axial collapse because the deformation load is maintained at a high value and continues up to a high-deformation stroke while going through repeated maxima and minima.^5,7)

Fig. 7

Typical examples of collapse progression recorded with a high-speed video camera and final shape of the column for steels A, B and C.

For steel B, fracture at the buckled region near the upper end was clearly observed at 20 ms. The top of the column was forcibly displaced without new folds being generated in the adjacent region, and therefore, after 30 ms, collapse proceeded through tearing of the column. The occurrence of significant fracture is undesirable because it makes the deformation mode and deformation load difficult to control.

For steel C, buckling was generated near the upper end at 10 ms, but at 20 ms, the column bent toward the front without generating new buckling, and thereafter deformation progressed through overall collapse of the entire column. The axial load dropped sharply when this overall collapse occurred. The occurrence of bending mode deformation is also undesirable, because energy absorption is less efficient than in accordion type deformation.⁷⁾

Table 3 summarizes the test conditions for the collapse tests and the results of judgment regarding the collapse mode for all the columns tested. Columns exhibiting an accordion shape were expressed as “Accordion”. Among these, it was possible to identify compact mode, which shows an overall and largely uniform accordion shape (as seen with steel A in Fig. 7), and noncompact mode,¹⁶⁾ which has an accordion shape but contains partly non-uniform regions. In Table 3, these are distinguished as “AC” and “AN”. “Fracture (F)” corresponds to columns in which, although one or two folds occurred, fracture was prominent, as seen with steel B in Fig. 7. Some columns exhibited buckling only in the initial stage of collapse and deformed by bending mode without the formation of progressive folds, as with steel C in Fig. 7, and these were classified as “global bending (GB)” in accordance with the expression adopted by White and Jones.⁶⁾ GB was often accompanied by fracture of the material, which is expressed as GB + F in Table 3.

Table 3 Conditions and deformation mode of the specimens in the axial collapse experiment.

As stated in section 2.1, the columns used in this study were given a flat rectangular cross-section,⁷⁾ which tends not to be deformed into a uniform accordion shape, in order to clarify the difference in deformation behaviors between differing materials. Therefore, although there was no material for which all the tested specimens exhibited a uniform accordion shape, the differences in deformation behavior between the materials were clearly demonstrated. For steel A, the ratio of columns exhibiting accordion type deformation (AC or AN) was high regardless of the test conditions, and no column was classified as Fracture (F). In contrast, for steel B, which has the same level of UTS as steel A, the ratio of Fracture (F) was generally high, although accordion type deformation was observed in one column under high impact velocity conditions. With regard to the class 980 MPa materials, steel D had a higher ratio of accordion type deformation than steel C when compared under the same test conditions (test No. 7 to 11). Steels A and D, which showed a high ratio of accordion type deformation, both exhibit YPEl, although their UTS and n-values are different. Hence, steels that exhibit YPEl tend to collapse into a stable accordion shape.

Next, focusing on steel A and B, we show the results for deformation behavior in the early stage of collapse. Figure 8 shows the appearances of two hat columns made of steels A and B after deformation to a displacement of 50 mm at an initial impact velocity of 22.5 km·h⁻¹. Two pictures of the same column were taken from different directions for steel A. Here, one fold occurred at the upper end, and, as shown by the white arrows, slight undulations or wave-like deformations formed at regular intervals on the top surface, side surface and flanges of the hat section over the entire length of the column. In contrast, for steel B, the areas other than the buckled region at the bottom of the column appear straight, with almost no visible deformation.

Fig. 8

Appearance of the hat columns of steel A and steel B after axial collapse to a displacement of 50 mm.

Next, focusing on fracture of the buckled region, hat columns made of steels A and B were deformed quasi-statically to a displacement of 20 mm so as to form only one fold, and the bending radii of the bucked regions were measured. The buckled region of steel A had a bending radius of 1.55 mm and no fracture was observed, but fracture was observed inside the buckled region of steel B. Figure 9(a) shows the appearance of the steel B column after formation of one fold. Figure 9(b) shows the inside of the buckled region cut from the steel B column at the position indicated by the rectangle in Fig. 9(a). For this cut specimen, part of the back plate was removed, and the picture was taken from the back side of the column. As indicated by the black arrow in the figure, a crack has formed along the bend line. The bending radius at another bend line without fracture was measured as 1.30 mm, which was smaller than that for steel A.

Fig. 9

Hat column made with steel B deformed for 20 mm by quasi-static compression: (a) appearance of the column and (b) cut specimen showing fracture along the bending line at the buckling region.

4.2 Bending test simulating accordion type deformation region (BCE)

Figure 10 shows the appearance of the BCE specimens deformed until fracture occurred, observed from the edge of the specimens. Fracture occurred along the bend line. The specimen made of steel E, which has a high n-value, deformed into a U-shape with a large bending radius. In contrast, the specimen made of steel F, which has a low n-value, exhibits a small bending radius. This is thought to be because the region of plastic deformation is larger for high n-value materials, so that the strain near the bending line readily dispersed.

Fig. 10

Appearance of the test pieces simulating the basic collapse element: (a) steel E and (b) steel F.

From the experimental results described above, it has been demonstrated that during axial collapse of ultra-high strength steels: (1) steels exhibiting YPEl are easily deformed into a stable accordion shape, due to small plastically deformed regions formed at regular intervals in the early stage of collapse, (2) a continuous accordion shape cannot be achieved if significant fracture occurs in the buckled region, and (3) the shape of the buckled regions is affected by the n-value of the material. In the following sections, we will discuss the experimental results using the results of numerical simulations.

4.3 FEM simulation of axial collapse

First, we will present and discuss simulation results that focus on the buckling start point in the early stage of collapse. Figure 11 shows the distribution of equivalent plastic strain in the column after 4 ms of deformation (deformation amount: 22 mm) obtained from a simulation of axial collapse in which the effect of YPEl was investigated. Here, one fold was observed regardless of the amount of YPEl. In addition to this buckling, small regions of plastic deformation with strains of 3% to 7% were observed in the other areas. These regions of small deformation were seen only in the vicinity of the buckled region in the material with no YPEl, but tended to become dispersed throughout the column as the amount of YPEl increased. In the material with 4% YPEl, the deformed regions existed at regular intervals throughout the column. This result is consistent with observation of the steel A column shown in Fig. 8. The regions of small deformation generated in the early stage of collapse seem to act as the starting points for buckling, in a similar manner to crush beads, resulting in the promotion of stable accordion type deformation.

Fig. 11

Contour maps for equivalent plastic strain of the hat columns deformed for 4 ms obtained by the FEM simulation of axial collapse.

During axial collapse, stress waves are generated at the top end due to collision of the falling weight, repeatedly propagate along the longitudinal direction of the column, and are reflected at the opposite end.¹⁷⁾ Plastic deformation occurs at the locations where the stress level exceeds the elastic deformation limit of the material. In the case of a material that exhibits YPEl, strain increases rapidly to the YPEl level when the stress reaches the yield strength. Therefore, it is believed that generation of regions of small deformation becomes more significant as YPEl increases.

4.4 FEM simulation of “free bending”

Next, we will focus our discussion on the shape and fracturing of the buckled region. In the results for the BCE specimens shown in Fig. 10, the shape of the buckled region, especially bending radius, was different depending on the n-value of the material. In order to clarify the reasons for this, we now present the results of free bending simulations relating to material properties and bending behavior. Figure 12 shows the distribution of plastic strain in specimens made of steels A and B after “free bending” deformation. After 15 ms of deformation, with the amount of deformation still small, there was no clear difference in strain distribution between steels A and B, but as deformation time increased up to 20 ms and 50 ms, a clear concentration of strain occurred at the center of the steel B specimen. The bending radius r at the center of the specimen is indicated in the figure, and is clearly smaller for steel B. This supports the experimental results shown in Fig. 10. We can therefore deduce that, in steel A, which exhibits a high degree of work hardening after YPEl, dispersion of the strain gives a large bending radius, whereas in steel B, which has a small n-value, the strain is concentrated locally in the region of the bend, giving a small bending radius.

Fig. 12

Contour maps for plastic strain of the bent specimens obtained by “free-bending” simulation, at the deformation periods of 15 ms, 20 ms, and 50 ms. r: Bending radius at the center of the specimen.

4.5 Material properties required for stable deformation during axial collapse

In this section, based on the results described above, we describe the material properties required for stable deformation during axial collapse. Achieving sequential formation of folds during axial collapse requires: (1) easy generation of buckling start points in the early stage of collapse, (2) avoidance of fracture in the buckled region and (3) avoidance of the “global bending” mode. First, YPEl of the material is effective for generating buckling start points. The FEM simulation results shown in Fig. 11 indicate that buckling start points form throughout the column if the material has a YPEl of 4%. As shown in Table 3, 80% of the columns made of steel A, which has a YPEl of 4.7%, deformed into an accordion shape, whereas that ratio decreased to 40% in steel D, which has a YPEl of 2.5%. From these results, it may be concluded that YPEl needs to be 4% or more in order for the columns used in this study to be deformed into a stable accordion shape. However, this value will vary depending on the shape and dimensions of the column.

Second, it is important to avoid fracture in the buckled region. If fracture occurs, load transmission to the adjacent region becomes insufficient and sequential formation of folds becomes difficult. Whether or not the fracture occurs depends on the difference between the critical bending radius of the material and actual bending radius of the buckled region. A material with a high n-value and small critical bending radius is ideal. However, as shown in Table 1, the critical bending radius in the U-bend test on steel A, which exhibited stable accordion type deformation with the lowest occurrence of fracture, was inferior to that of steel B, which exhibited the highest occurrence of fracture. This is believed to be because, for steel A, which has a higher n-value than steel B, the bending radius at the buckled region deformed through “free bending” was larger than for steel B, so that this radius was larger than the critical bending radius for steel A, but smaller than the critical bending radius for steel B. In addition, steel D has a low n-value and small bending radius in the buckled region, but since it exhibits good bendability, fracture is considered unlikely to occur. Therefore, the balance between n-value, which affects the bending radius in the buckled region, and the critical bending radius of the material is important for avoiding fracture in the buckled region during axial collapse.

Finally, we discuss the ease with which overall collapse of the column occurs. The occurrence of overall collapse also makes it difficult to transmit the load from the buckled region to the adjacent area and generate sequential buckling. Although steel D had the second highest ratio of accordion type deformation after steel A, global bending occurred more frequently than in steel A. Steel D exhibits YPEl, but this is smaller than that for steel A, so that, compared to steel A, it is thought that there were fewer regions of small deformation that could act as buckling start points during the early stage of collapse, resulting in deformation being concentrated in the buckled region and making overall collapse occur more readily in steel D columns. Furthermore, having a smaller n-value than steel A may be related to overall collapse of the column. It has been reported that in low n-value materials, deformation is concentrated in the initial buckled region making it difficult for sequential buckling to occur, so that overall collapse is more likely.^9–11) It is thought to be for this reason that the ratio of accordion-shaped deformation for steel D, which has a low n-value, was lower than for steel A. As can be seen from the above discussion, n-value is an important material property with regard to stabilizing axial collapse performance. However, this study has not determined the existence or otherwise of a limit on n-value, or the strain range in which the n-value should be taken into account, and so these remain as topics for future research.

5. Conclusions

In this study, high-speed axial collapse tests were performed on hollow columns with hat cross-sections made of various ultra-high strength steel sheets with different n-values, UTS, bendability and s–s curves, and the effects of mechanical properties on the axial collapse stability were clarified. The results obtained are summarized below.

1. (1)    Columns made of steels that exhibit yield point elongation gave a higher ratio of accordion-shaped deformation. For these materials, regions of small deformation have already formed throughout the column when buckling occurs in the early stage of collapse, and it is believed that these act as start points for buckling that promote the sequential formation of folds, resulted in stable accordion type deformation.
2. (2)    When significant fracture occurred in the buckled region in the early stage of collapse, there was little further buckling in the adjacent region due to load transmission to that region being insufficient, and stable accordion type deformation was not achieved.
3. (3)    Increasing the n-value of the material to suppress strain concentration in the bend region, and improving the bendability of the material were shown to be effective for avoiding fracture.
4. (4)    Among the materials that exhibit yield point elongation, accordion type deformation was achieved more frequently in materials with a high n-value. This is thought to be because strain concentration in the buckled region is suppressed and load is transmitted effectively to the adjacent region, thereby promoting sequential formation of folds and resulting in accordion type deformation.
5. (5)    It was shown that steel sheets which exhibit yield point elongation and have high work hardening capability allow stable accordion type deformation to be achieved during axial collapse, and can therefore contribute to improved crash performance of parts designed for axial collapse.

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