Innovative solution for strength enhancement of metallic like-composite tubular structures axially crushed used as energy dissipating devices

Thin-Walled Structures 119 (2017) 332–344

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Innovative solution for strength enhancement of metallic like-composite tubular structures axially crushed used as energy dissipating devices

MARK

⁎

A. Abdul-Latifa,b, , A. Ahmed-Alia,c, R. Baleha,d, M. Ould Oualic a

Laboratoire Quartz, Supméca, 3 rue Fernand Hainaut, 93407 St Ouen Cedex, France Université Paris 8, France c Laboratoire LEC2M, University Mouloud MAMMERI of Tizi-Ouzou, BP17RP, 15000 Tizi-Ouzou, Algeria d Ens. Sup. La salle Passy-Buzenval, Rueil-Malmaison 92500, France b

A R T I C L E I N F O

A B S T R A C T

Keywords: Plastic buckling Case-hardened forms Quasi-static loading Energy absorber

This work presents the milestones of the underlying of a patented work [1] (Abdul-Latif, 2014) which aims to enhance the plastic buckling resistance of thin-walled right-circular cylindrical mild steel tubes deformed axially under the quasi-static compressive load. The proposed concept can be described by producing a metal likecomposite where a hard phase incorporates in these tubes made by case-hardening of 15% of tubes outer surface with different geometrical shapes and a constant depth along the tubes thickness. To study the effect of casehardening configurations, several forms were designed, made and tested. They were four ring forms (with 2, 3, 4 and 5 rings), two vertical strip forms (2 and 3 strips) and, six helical strip forms with three tilt angles of 30°, 45° and 60° (2H30, 3H30, 2H45, 3H45, 2H60 and 3H60). The total energy absorption of conventional tubes could be increased up to 46%. The effects of the case-hardened zone, quasi-static strain rate and the crush force efficiency were investigated. Moreover, the deformation modes of these case-hardened tubes were analyzed. The effect of the case-hardened forms could be classified into three categories by the gain percentage (low, intermediate and high gains). Especially in the high gain category, the material behavior seems to be directed by complicated local strain induced by the metal like-composite tube, where a triaxial strain state was encouraged particularly within the tube wall of 3H30. For this reason, the collapse load became the function of case-hardened forms.

1. Introduction

with its manufacturing process simplicity, i.e., low cost product. This leads therefore to economical energy-dissipating devices (e.g., [2–6]). Understanding the behavior of collapsed structures (modes of deformation and the resulted failure) and its materials behavior is essential to evaluate the energy absorption ability. According to the relevant literature, a strong conviction is emerging that the response of structures to a large extent depends on several factors such as the structural geometry, its material properties particularly strain hardening behavior, boundary and loading conditions, strain rate, etc. (e.g., [2,7–9]). It has been recognized that thin-walled components are widely used in these devices under compressive loading. Several deformation modes can be recorded. Actually, it can be plastically turned inside-out or outside-in. This is so-called tube inversion (e.g., [10–13]). It provides a favorable constant crush force, but with relatively low stroke efficiency. This is because only half of the tube length contributes in plastic deformation. Also, it has a strong sensitivity to external loading condition which makes its application limited as energy-dissipating system. On the other hand, tubes can be made to split and curl up (for

For several decades, the passive safety concept related to crashworthiness has received a significant attention in designing energy dissipating systems and devices. These systems should be able to answer the high requirements for crashworthy design of different transport vehicles with the aim of improving their safety and reliability. The role of such devices is to mitigate both structures damaging and human injuries during vehicles collusion. These devices can be used in many mechanical systems, like road vehicles, railway couches, aircraft, ships, lifts, machinery, satellite recovery, aircraft soft-landing, etc. One of these passive safety devices is one that use large deformations as a basic concept. This will be considered in the present work. The extensive crashworthy structural elements commonly used in these devices are different: circular and square tubes, honeycomb structures, spherical shells, frusta, taper tubes, s-shaped tubes, composite tubes, foam-filled tubes, wood-filled tubes, etc. The cylindrical tubes attract much more attention due to an optimized combination of several key factors of high stiffness/high strength/low weight together

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Corresponding author at: Laboratoire Quartz, Supméca, 3 rue Fernand Hainaut, 93407 St Ouen Cedex, France. E-mail address: [email protected] (A. Abdul-Latif).

http://dx.doi.org/10.1016/j.tws.2017.06.024 Received 28 March 2017; Received in revised form 3 June 2017; Accepted 22 June 2017 0263-8231/ © 2017 Published by Elsevier Ltd.

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loaded structure due to changes in local deformation mechanisms [37]. The reported results of copper circular shells buckling revealed an increase in the energy absorption up to 60% compared to the classical uniaxial case. Whatever the energy dissipating device type, especially for these devices used the plastic buckling basis, a well-grounded question is worthy to be answered. This is regarding the possibility to further increase the energy absorbed in a tubular structure crushed axially. In this work, the performance of axially crushed mild steel tubes could be enhanced using an innovated idea [1]. It consists of creating steel likecomposite with different geometrical configurations. The steel likecomposite could generate complex straining conditions within the structure through the combination of local heterogeneities dictated by the composite and the external load. Undoubtedly, mild steel tubes are employed due to its ability to be case-hardened up to a certain depth along the tubes thickness. In this work, the targeted case hardening involves surface and subsurface modification without any increase in tube dimensions. Hence, it is a technique by which the outer surface hardness of steel alloys part is improved by a carburizing or nitriding process without affecting the tough interior of the part. A carbonaceous or nitrogenous atmosphere is used at elevated temperature to treat any steel part at its outer surface level by atomic diffusion. With this diffusion, the chemical composition of the surface is modified by adding hardening elements such as carbon, nitrogen, or boron. The thickness of case hardened zone is usually on the order of 1 mm which is harder than the inner core of material. Selective a surface-hardening zone, as in this study, allows localized hardening. One of the important advantages is the compressive residual stresses which are induced at the surface of the case-hardened part. Such a stress type reduces the crack initiation probability that helps prevent crack propagation at the casecore interface particularly in fatigue [38]. Likewise, this combination of hard surface and tough case-core is helpful for several mechanical elements such as cams, gears, bearings, shafts, automotive elements to resist the impact that occurs during operation. Several carburizing processes have been already developed which are: gas carburizing, vacuum carburizing or low-pressure carburizing, plasma carburizing, salt bath carburizing, pack carburizing. Such methods have their limitations and advantages. However, gas carburizing is now considered as the most effective and widely used method for carburizing steel parts in high volume. In this study, 15% of tubes outer surface was chosen and heat treated with several shapes. A key point that emerges from this study is related to the structure response (i.e., plastic flow mechanism, the energy absorbed and crush force efficiency) which is largely influenced by the treated shape. To study the geometrical effect of case-hardened forms, they are: four different ring forms (2, 3, 4 and 5 rings), two configurations with 2 and 3 uniformly distributed vertical strips parallel to the tube axis and finally 2 and 3 helical strips with three tilt angles of 30°, 45° and 60°. The behavior of the crushed materials demonstrates the dependence of the plastic buckling behavior on the composite type.

example, [14–17]). It is found that axial splitting and curling of tubes provide low crush load and low stroke efficiency. Therefore, these devices provide us with low specific energy absorption. To the authors knowledge, the first reported work on the plastic buckling of thin-walled tubes under axial compression has been pioneered by Mallock in 1908 [18]. Currently, this concept is largely used in developing energy dissipation devices. Note that the goal of this work falls into this category. Circular, square and rectangular sectioned tubes are the most widespread and efficient means of dissipating energy (e.g., [19–25]). The recorded load-deflection curve has an oscillatory nature with a first maximum peak load. The latter is considered in determining the crush force efficiency (ρ) as a factor for evaluating the crashworthiness of an energy absorber device. Its definition and role will be discussed later. For a given tube, the peak load is affected by initial imperfections over the tube. To minimize its value, several solutions have been developed, like holes near the tube ends, chamfering, grooving, etc. The concept of a buckling initiator is successfully developed reducing this peak load up to 30% [24,25]. This device, in the process of large plastic deformations, provides one of the best due to: (i) the stability of the average collapse load throughout the entire crushing process and (ii) the available stroke per unit mass, i.e., a high percentage of tube material contributes to the plastic deformation of the tube wall. The bending and stretching strains combination and its progress along the buckled tube guarantees the participation of material in the absorption of energy by plastic work. Three principal collapse modes could be observed: axisymmetric mode, diamond mode and mixed one. The main geometrical parameters controlling these modes are: the η (= R/t) ratio of diameter (R) to thickness (t) and the λ (= R/L) ratio of diameter to length (L) [21,26,27]. For η < 15 [2], the mode axisymmetric becomes predominant for most engineering materials. Nevertheless, the diamond fold mechanism (or mixed one) tends to occur for larger values. Favorable crashworthiness characteristics could be achieved when the tube deforms in axisymmetric mode, i.e., the energy absorbed is gaining more recognition in the axisymmetric mode than that in the diamond or mixed one [27]. Together with η ratio, the λ ratio can also play a significant role in controlling the plastic flow mechanism. Few investigations have been carried out to determine the effect of this parameter on the axial collapse of tubes (e.g., [21,26,27]). In the light of this fact, a new solution has been proposed for encouraging the axisymmetric mode. In fact, the developed solution consists of cutting a tubular structure in several portions. These portions are coaxially assembled together and separated by non-deformable discs. The number and the length of portions effects (i.e., λ ratio) on the flow mechanism have been investigated [27]. Besides, other solutions have been already proposed with the purpose of not only maximizing the energy absorbed but improving the stabilization of the collapse process. The idea is always based on the concept of encouraging the axisymmetric mode. These developments deal with either introducing corrugations over the tube to force the plastic deformation to occur at predetermined intervals along the tube length (e.g., [28,29]), or introducing circumferential grooves which are cut alternatively inside and outside of the tube at predetermined intervals. This offers an effective solution to orient the plastic deformation occurring at these predetermined intervals along the tube [30–34]. These methods provide a reasonable increase in crush force efficiency of the developed shock absorber, but with relatively limited stroke efficiency. This is due to the fact that part of the tube length cannot contribute in plastic deformation especially of the circumferential grooves solution and nondeformable discs. In general, limited research programs have been conducted for controlling the deformation mechanisms. Therefore, this field still requires more attention. Contrary to these standard passive systems, a relatively new concept has been developed to generate a plastic biaxial buckling regime via a patented rig [9,35,36]. The solution deals with creating a particular combined biaxial complex loading condition of compression-torsion. Hence, this provokes an enhancement in strength properties of the

2. Originality and general scoop In these tubular structures, as demonstrated before [e.g., [9,35,36,39]], enhancement the material performance through the loading complexity is a concept that requires further development henceforth beside the common structural design requirement. In the same state of mind, the originality of this study deals with the enhancement of the energy dissipating capacity of thin-walled cylinders loaded axially by modifying the mechanical behavior of the material in some targeted zones starting from the outer surface of the tubular structures up to a certain depth. This can be made using a specific casehardening process. Afterwards, the obtained tubes are considered as a steel like-composite (i.e., increase the tube strength in selected zones for certain depth and form). It is so-called steel like-composite, since the product cannot be a conventional composite material. Designing 333

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several forms of targeted zones is a key factor since it has an important impact on the plastic buckling behavior of these tubes. Hence, the whole idea represents an innovative concept leading to a significant improvement in the energy dissipating capacity for tubes plastically buckled [1]. Actually, mixing of two phases of different mechanical properties of the same tube wall (hard and soft phases) leads to a substantial enhancement in the energy absorption during plastic buckling. With these geometrically complicated configurations of the case-hardening, the tubes are plastically deformed with particular and complex strain state condition enhancing consequently its energy dissipating capacity. Particular attention has been paid to several key features related to the case-hardening process (depth, form, and volume fraction of the case-hardened area with respect to the outer tube surface). These factors were investigated since the plastic buckling behavior of thin-walled tube is highly influenced by these features. For a given case-hardening volume fraction and case-depth, the form of the carburized area is a key parameter which has been investigated in this study. Thus, several casehardened forms were designed and tested.

Table 2 Mechanical properties of the reference material.

3.2. Heat treatment: case-hardening The mild steel could be easily heat-treated by case-hardening process during which the chemical composition of its surface is modified. As a key factor, the depth of carburized zone is governed by heating temperature, holding time, steel chemistry, and initial available carbon at the surface. To reduce strongly the holding time, carburizing could be conducted at temperature above 980 °C [38]. The process terminates when the high-carbon surface layer was quenched, whereas the specimen core remains low-carbon steel. In this study, a low pressure gas carburizing treatment is utilized by means of a furnace. Heated up by uniform radiation, specimens were therefore surrounded by a continuous carbon-bearing atmosphere for maintaining a high carbon potential under operating temperatures of 970 °C and holding time of 2 h. The targeted case-depth was almost uniform of 0.5 mm. Then, specimens should be transferred to a quench chamber and cooled by high pressure neutral gas to minimize the induced distortion to the lowest possible level (e.g., [40]). Since this type

P

≤ 0.17

≤ 1.20

≤ 0.35

≤ 0.035

≤ 0.030

205,000

≥ 235

360–470

26

3.4. Material phases characterization After heat treatment, characterization of the already carburized and protected zones was carried out by three steps: (i) Local analysis showing the evolution of mild steel microstructure induced by the casehardening; (ii) Microhardness evaluation throughout the tube wall thickness with the presence of the case-hardened area and (iii) Mechanical characteristics of the different phases using standard tensile

Table 1 Chemical composition of the as-received mile-steel. S

Elongation (%)

The designed case-hardened forms were characterized by various forms, dispatched equidistantly with a symmetry regarding either the radial or axial direction (Fig. 1). Technically, they could be classified into three principal categories noted by nR, nV and nHα, where n indicates the number of strips, R ring form, V vertical strip, H helical strip and α helical strip tilt angle. The ring forms are referred to by: 2R, 3R, 4R and 5R, arranged equidistantly over the entire tube length. The second category deals with longitudinal strips over the entire tube length and arranged regularly and parallel to the tube axis. So, two cases were proposed and studied which are 2V and 3V. The third category concerns helical strips of three configurations defined by three helicoid angles of 30°, 45° and 60° with two values of n (n = 2 and 3). This yields 6 configurations noted by: 2H30, 3H30, 2H45, 3H45, 2H60 and 3H60. Table 3 summarizes the three categories of designed casehardened forms. Two other configurations represent the upper and lower bounds noted by Ref and CH-T. In fact, Ref is the case of asreceived tube (lower bound), while CH-T represents the upper bound where the outer tube surface is totally case-hardened. After determining the selected case-depth of 0.5 mm, the fundamental issue was related to define the volume fraction and the form of case-hardened zones. To get the targeted case-hardened area of 15% of the tube outer surface, a suitable protection of the remaining outer surface together with the inner one (non-hardened zones) was therefore carried out by a special paint coating (LUISO W36) to generally preserve its initial microstructure after heat treatment. Cleaning and degreasing operations were made before the heattreatment. The targeted case-hardened areas need to be initially covered by adhesive tapes before the paint coating. The distribution of these tapes was determined by the case-hardened form. The geometrical complexity and their precision require machining of different specific jigs (Fig. 2) to aid the positioning of these adhesive tapes (Fig. 3). This coating was carried out by immersing the tubes in a tank filled with this paint solution. After 10 s of holding, tubes are then removed to dry them in open air. The adhesive tapes should be removed after drying to reveal the surfaces that will be carburized (Fig. 4). The whole prepared specimens were charged in the carburizing furnace in a single batch to ensure the uniformity of the treatment. Finally, a conformity check of the process was made.

Judicious material selection is an important step to meet the requirements for getting two phases (hard and soft) in each structure with suitable ductility. Accordingly, the mild steel represents a less expensive low-carbon steel which is considered as an appropriate option for generating a steel like-composite. This steel shows a wide range of plastic deformation, i.e., yielding a good plastic energy dissipating capacity. In this event, non-welded single length tubes (referred to reference) made of commercial mild steel were employed, designated according to French standard as NF EN 10297-1 and NF A 49310. Table 1 summarizes their chemical compositions determined by wet chemical analysis. The mechanical characteristics are given in Table 2. A single thin-walled tubular geometry of 15 mm internal radius (R), 1 mm thickness (t) and 80 mm length (L) was employed. Such dimensions leading to radial (η = R/t) and longitudinal (λ = R/L) ratios of 14.5 and 0.18, respectively.

Si

σmax (MPa)

3.3. Specimens preparation

3.1. Tested material

Mn

σy (MPa)

of treatment requires specific equipment, therefore this operation was conducted in a French company (BODYCOTE) specialized in advanced heat treatments. To study the effect of the carburized volume fraction, only 15% of the outer tube surface is treated. This was a rather random choice whose main purpose is to create the two phases alternating between relatively soft and hard zones for maximizing the energy absorbed during plastic buckling.

3. Experimental methodology

C

E (MPa)

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Fig. 1. Plots showing schematically the case-hardening designed forms on the outer surface of tube.

Table 3 Different case-hardening configurations. Geometrical forms of the casehardened areas

Different configurations

Strip width (e), mm

Strips in the form of rings (R)

2 3 4 5 2 3 2 3 2 3 2 3

6 4 3 2.4 7.06 4.7 6.1 4.08 5 3.3 3.5 2.3

Vertical strips (V) Helical strips (H)

30° 45° 60°

Rings (2R) Rings (3R) Rings (4R) Rings (5R) Vertical strips (2V) Vertical strips (3V) Helical strips (2H30) Helical strips (3H30) Helical strips (2H45) Helical strips (3H45) Helical strips (2H60) Helical strips (3H60)

Fig. 4. Tubes after their protection showing some targeted case-hardened zones.

Fig. 5. Schematic presentation of the typical tensile test specimen (dimensions in mm).

tests. Note that several tensile test specimens were made from the asreceived mild steel. Two heat treated cases were conducted which are totally carburized and fully protected specimens as well. They were treated together with the tubes in the same batch. The typical tensile specimen geometry is schematically presented in Fig. 5. Three selected zones throughout a tube wall section located at both wall extremities, i.e., internal and external, and at the center were investigated as shown in Fig. 6. Local analysis was conducted on the as-received (Ref) and casehardened specimens using the three selected zones a, b and c (Fig. 6). In the case of as-received tube and whatever the selected location, the observed microstructures demonstrated the presence of two intended phases: ferrite as a dominant phase and perlite (Fig. 7a). As far as the case-hardened specimens are concerned, a significant change has been observed in the material microstructure induced by the heat treatment. Indeed, an increase in the volume fraction of perlite has been demonstrated compared to the ferrite at the protected surface (inner part) of the tube. This seems to be due to the continuity of the diffusion which slows down slightly towards the inner surface of the tube (Fig. 7b- zone a). In the tube wall center (Fig. 7b- zone b), it was obvious that the ferrite percentage becomes more important than that in zone a. Moreover, on the case-hardened surface (outer part), the martensitic phase

Fig. 2. Different realized jigs for positioning the adhesive tapes.

Fig. 3. Examples showing the adhesive tapes positioning on the tube outer surface according to designed form before applying the protected paint.

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Fig. 6. Schematic presentation of tube section showing the three selected locations for characterizing different material phases. Fig. 8. Microhardness profiles throughout the tube wall thickness before and after heattreatment.

was evidently dominant with the formation of the secondary cementite at the grain boundaries surrounding the martensitic grains (Fig. 7bzone c). The hardness evolution is described in Fig. 8 using the Vickers microhardness technique. Indeed, the microhardness profiles before and after treatment were evaluated and compared by ten measurements for each case throughout the tube wall thickness. These measurements were conducted with equidistance, where the first measurement was made in the vicinity of the outer surface and the last one at the edge of

the internal surface of the tube. The microhardness of reference tube was almost constant having an average value of HV = 157. Whereas, for the case-hardened tube, the microhardness varied between a minimum value of HV = 247 (for protected inner surface) and HV = 383 as a maximum value (for the external case-hardened surface). The hardness evolves gradually in an almost linear fashion from the 6th position approaching the external surface where the hardness attains its

Fig. 7. Micrographs showing the microstructure evolutions for the three selected locations related to: (a) the as-received mild steel; (b) after the case-hardening process.

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Table 5 Overview of the deformation modes for the case-hardening configurations.

Fig. 9. Engineering stress-strain curves for carburized, protected and reference states.

maximum value, i.e., HV = 383. It evolved consequently with 55% between these two extreme values in the case of case-hardening. The maximum increase was of 144% compared to the reference tube hardness. These results are in perfect accordance with the microstructural observations where more martensite phase is found on the external surface. Using tensile tests under a quasi-static strain rate of 10−3/s, the cases of as-received, completely protected and totally case-hardened for both inner and outer surfaces were studied. Fig. 9 shows their corresponding engineering stress-strain curves where evident differences in their mechanical behaviors were recorded. Indeed, a high work-hardening for the totally case-hardened case was observed followed by the protected and as-received cases, respectively. Moreover, it was recognized that the work-hardening of the carburized structure evolves steeply and relatively slowly for the other cases. Table 4 sums up the principal mechanical properties of these three cases, Young's modulus, yield stress, tensile strength and the relative elongation. As expected, the carburization process modifies the mechanical properties due to the change in material microstructure. It could be concluded that with these characterization techniques, a structural transformation gives rise different combined properties of work-hardening and its rate, hardness and ductility throughout the wall thickness. Because of the adopted case-hardening, the enhancement of the energy dissipating capacity of tubes could be interpreted by a change in the material mechanical behavior in some well-defined zones on the outer surface and it will be discussed below.

Different configurations

Deformation mode

Ref 2R 3R 4R 5R 2V 3V 2H30 3H30 2H45 3H45 2H60 3H60

AM DXM DXM DXM DXM AM DXM DM AM DXM DXM DM AXM

Using these valid tests, mean force-deflection curves are then presented.

4. Results and discussion 4.1. Flow mechanisms As energy absorber, the tubular structures axially loaded by quasistatic or dynamic strain rates have been the topic of wide studies since 1908 [18]. Thus, they could deform in four possible deformation modes whatever the applied strain rate: axisymmetric mode (AM), diamond mode (DM), mixed mode (XM) and Eulerian mode (EM). The generation of these modes are mainly governed by the radial (η = R/t) and longitudinal (λ = R/L) ratios and their interaction [27]. The recorded energy absorbed is affected by the deformation mode for a given strain rate. The Eulerian mode should be avoided by controlling the λ ratio for a given value of η. Note that the AXM and DXM notations represent the mixed mode with axisymmetric and diamond predominance, respectively. The plastic energy is administered by the plastic hinge zones which localize differently depending, in this work, on the case-hardening and deformation mode as well. Recapitulative resulted modes are summarized in Table 5, where the majority of tests generate mixed modes (DXM: 2R, 3R, 4R, 5R, 3V, 2H45 & 3H45 and AXM: 3H60). However, purely AM (Ref & 3H30) and DM (2H30 & 2H60) were observed. Since only single tube geometry was employed, the proportion of axisymmetric and diamond in the mixed mode was therefore directed by the case-hardened form. Some general observations may be made on the crashworthy behavior of the tubular structure. In fact, Fig. 10 shows a typical example of load-deflection curve where some stages during axial compression were selected illustrating corresponding views of progressive collapse of the 3H30 case. Obviously, this example demonstrates a flow

3.5. Experimental procedure The employed tubular structures were examined in a progressive axial crush study. They loaded between the two parallel platens of an Instron Universal Testing Machine (type 5582) under two constant compressive cross head speeds, namely 5 and 500 mm/min at room temperature. The machine, where each steel like-composite thin-walled tube was correctly positioned between these two platens, was connected to an acquisition chain to simultaneously record the force and the corresponding displacement during tube crushing process. Thus, the results reliability was widely acceptable. As an adopted approach to ensure the experimental results accuracy, each test was repeated, at least, six times under the same experimental conditions (applied speed and room temperature). If the differences in responses among, at least four of the six tests exceed 3%, then other tests should to be conducted. Table 4 Mechanical properties of three studied cases.

As-received tube Protected tube Carbonized tube

E (GPa)

σy 0.2 (MPa)

σmax (MPa)

Elongation (%)

205 206 209

223 331 602

381 505 1163

24.8 15.5 10.3

Fig. 10. Typical example of load-deflection curve of plastic buckling of 3H30 casehardening configuration showing the corresponding views of progressive collapse.

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Fig. 11. Photos showing the plastic buckling progress up to the end of tube crushing for different ring forms: (a) 2R; (b) 3R; (c) 4R; and (d) 5R.

deformation onset. With regard to the case-hardening of vertical strips, Fig. 12 illustrates the successive plastic buckling mechanism of 2V and 3V tubes. Obviously, the 2V case deforms purely by AM (Fig. 12a); whereas 3V behaves differently with DXM starting with AM for two folds followed by DM up to the final stage (Fig. 12b). Concerning the case-hardening of helical strips with inclination angle of 30°, the successive plastic buckling mechanism of tubes is described in Fig. 13 for both 2H30 and 3H30 tubes. In 2H30, a purely DM was recorded (Fig. 13a); whereas AM was totally captured throughout the crushed length of 3H30 (Fig. 13b). It seems that these two distinct flow mechanisms were dependent of the case-hardened form which induces a local straining complexity within the material leading to a change in material behavior. For the case-hardening of helical strips with 45°, whatever the strips number, i.e., 2H45 or 3H45, the recorded deformation mode was always DXM (Fig. 14). Regarding the case-hardened of helical strips with inclination angle of 60°, the plastic buckling mechanism was displayed with purely DM in 2H60 (Fig. 15a). Nevertheless, Fig. 15b shows, for 3H60, a clear transition from AM to DM. Hence, one can generally conclude that the

mechanism of purely AM. Let us discuss the deformation modes for the studied cases generated in the course of crushing. For the ring forms, DXM was continuously recorded as shown in Fig. 11. The 2R type was characterized by a transition from AM to DM. Actually, two complete folds of AM were observed in the portion between the top extremity and the first ring (Fig. 11a). Due to the effect of the treated zone and its height, the third fold starts with DM in the middle portion between the two rings. And, the same deformation mode continued up to the final stage of the crushing. Moreover, the case-hardened zones resist, at the beginning, against plastic buckling and orient the deformation differently since these hard zones could lead to a partial discontinuity in the specimen wall. In the 3R and 4R cases (Fig. 11b and c), almost the same deformation scenario was recorded as before except that only one fold occurs constrained by the initial portion length which was less important than the above case. This did not permit the formation of more than one fold of AM, followed by DM throughout the remaining length. However, in 5R configuration (Fig. 11d), the plastic buckling start practically in the middle of the tube, precisely between the 3rd and 4th rings counting from the top. Hence, it represents a nonstandard 338

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Fig. 12. Photos showing the plastic buckling evolution during tube crushing for vertical strips configurations: (a) 2V; and (b) 3V.

Fig. 13. Photos showing the successive plastic buckling up to the end of tube crushing for: (a) 2H30; and (b) 3H30 configurations.

Fig. 14. Photos showing the successive plastic buckling up to the end of tube crushing for: (a) 2H45; and (b) 3H45 configurations.

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Fig. 15. Photos showing the successive plastic buckling evolution during tube crushing for: (a) 2H60; and (b) 3H60 configurations.

Fig. 16. Loading rate effect on the collapse loading evolution versus the axial deflection for the reference tube.

deformation mode is significantly influenced by the case-hardened form leading therefore to a complex triaxial strain state (compression, bending and shear strains) within the tube wall.

4.2. Structural behavior of tubes The collapse loads, energy absorbed and their evolution are now discussed during crushing for a total axial deflection of 50 mm for the case-hardened forms. The effect of loading rate on the structural response was first investigated. Fig. 16 reveals that responses of the metal like-composite tubes don’t show, in general, a sensitivity to the used loading rates of 5 and 500 mm/min. Both rates are within the range of quasi-static strain rates. Therefore, all tubular structures of different case-hardened forms were tested under a cross-head speed of 5 mm/ min. It should be noted that the same tube configurations are currently

Fig. 17. Evolution of: (a) axial collapse load; and (b) energy absorbed versus the axial deflection for the different configurations of case-hardening.

Table 6 Overview of the peak and mean collapse loads, crush force efficiency (ρ), total energy absorbed and gain percentage for the employed case-hardening configurations. Low gain

Pmax, kN Pav, kN ρ = Fav/Fmax Total energy absorbed, kJ Gain, %

Intermediate gain

High gain

Ref

2R

2H45

5R

3V

2H60

4R

2H30

2V

3H6

3H45

3R

3H30

CH-T

32.7 19.4 0.60 0.97 –

39.0 23.4 0.60 1.17 20.6

42.0 23.6 0.56 1.18 21.6

41.4 24.2 0.58 1.21 24.7

44.0 24.9 0.57 1.25 28.9

43.9 24.9 0.57 1.25 28.9

42.6 25.5 0.60 1.27 30.9

44.6 25.6 0.57 1.28 32.0

42.1 25.9 0.61 1.29 33.0

43.0 26.4 0.61 1.32 36.1

44.7 26.4 0.59 1.32 36.1

45.9 27.9 0.61 1.39 43.3

48.1 28.2 0.59 1.41 45.4

66.0 31.3 0.47 1.56 60.8

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Fig. 18. Plots showing the classification of different case-hardening configurations in four district families and the evolution of mean collapse load (Pav) for: (a) rig forms, (b) vertical strips forms, (c) two helical strips forms and (d) three helical strips forms.

Fig. 19. Variation of (a) the mean collapse loads mean collapse loads, (b) of the crush force efficiency (ρ) for the selected case-hardening configurations.

tested under dynamic loading using drop hammer facilities and the results will be published in forthcoming paper. Since a single tube dimensions and single employed loading were employed, hence their results were exclusively directed by these forms showing important influences on the tubes behavior. In this regard, Table 6 sums up the mean collapse load (Pav), peak load (Pmax) and the crush force efficiency (ρ) versus case-hardened forms. As far as the gain in mean collapse load (or energy absorbed) is concerned, Table 6 points out all the tested configurations which could be classified according to their gain into three types: low (2R, 2H45 & 5R), intermediate (3V, 2H60, 4R, 2H30, 2V, 3H60 & 3H45) and high gain (3R & 3H30). The load–deflection curves for these case-hardening configurations are plotted in Fig. 17a. The energy absorbed calculated by measuring the area under the recorded load–deflection curves and presented in Fig. 17b. Test results summary was also presented in Table 6. A simple optimization approach was adopted where all the tested configurations were divided and classified into four different families

Fig. 20. Evolution of axial collapse load versus the axial deflection for the selected casehardening configurations having the best mean collapse loads.

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Fig. 21. Evolution of axial collapse load versus the axial deflection for the selected configurations for: (a) stage 1, (b) stage 2, (c) stage 3, (d) stage 4 and (e) stage 5.

Fig. 22. Histograms showing the impact of the different case-hardened forms on the percentage of the gain attributed to specimen local behavior change. Fig. 23. Plot showing the impact of the different case-hardened forms on the mean collapse load and the total energy absorbed under a crosshead speeds of 5 mm/min.

(Fig. 18). In fact, this approach was conducted on the rig forms tubes where their mean collapse loads were plotted. In fact, Fig. 18a points out that the 3R tube has the highest mean load. Moreover, the two vertical strips cases (2V and 3V) reveal that 2V has the best mean load 342

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with which the 2R tube behavior was considered giving us the lowest gain. This gain assumes to be entirely affected by the presence of the hard zone only (rule of mixtures), i.e., no gain due to the local behavior change. It is known that this effect is quantified by 20.6% (Table 6). Now, the analysis consists of extracting this value from the values of all other cases. This difference would result from the effect of local change in material behavior governed by complex local straining. Fig. 22 shows the gain in percentage attributed to this change. Note that 2H45 and 5R have gains less than 5% which confirms the low gain case as already given in Table 6. On the other hand, the gains in 3V, 2H60, 4R, 2H30, 2V, 3H45 and 3H60 configurations varies by 15.5% > gain > 8%. They fall into intermediate gain category. The high gain (> 22.7%) was recorded for two cases which were 3R and 3H30 (Fig. 22). It is sufficient to be convinced to refer to Fig. 23 which summarize the overall results obtained by the various case-hardening configurations. Indeed, this figure classifies the mean loads and energy absorbed for all configurations in increasing order. One can thus observe the efficiency of this novel concept based on the case-hardening process. This efficiency of mean collapse load and total energy absorbed as well exceeds 45% for 3H30 tubes with respect to the classical tube (i.e., the reference).

(Fig. 18b). The helical strips were classified by two families according to the number of strips, i.e., 2H and 2H with their different inclination angles of 30°, 45° and 60°. It is obvious that the 2H30 was the best choice together with 3H30 (Fig. 18c and d). As a result, one can select the following forms: 3R, 2V, 2H30 and 3H30 having Pav = 27.9 kN, 25.9 kN, 25.6 kN and 28.2 kN, respectively compared to the reference configuration. Then, these mean collapse loads were plotted in Fig. 19a. It is shown that 3H30 has a highest value of Pav (see also Table 6). Due to a competition among these forms, it seems to be controlled by a local complicated strain state induced by these case-hardened forms, where a triaxial strain state was encouraged especially within the tube wall of 3H30. This issue will be discussed in more detail below. Keeping in mind that one of the important features for evaluating the crashworthiness of an energy absorber device is the ratio between mean load (Pav) and peak load (Pmax). It is so-called crush force efficiency (ρ = Pav/Pmax). This ratio represents a decision-making element in the design phase for such devices. Ideally, its value is equal to one. However, a significant decrease in this value poses a major problem related to the energy absorber device efficiency due to the contrast between these two loads. In practice, the role of such ratio is directly related to the peak load applied on protected occupants in a vehicle during the impact and whether it is below the designed tolerance level or not with a view to avoiding deadly injuries [41]. Table 6 shows the variation of ρ for all tested forms. Obviously, the worst case was related to CH-T with a value of 0.47; while the best value was 0.61 for 3R. Other configurations values vary from 0.56 to 0.6 (Table 6). Therefore, the CH-T case is not taken into account in the following discussion. Now, the validation of the 3H30 case through this ratio is essential. It is found that 3H30 has an acceptable ρ value of 0.59 (Fig. 19b and Table 6). Consequently, it could be recommended that the two tubes (3R and 3H30) represent the best ones among others as energy absorber devices, since the competition between them is always valid. Note that 3R was the best with respect to ρ and having a small difference with respect to 3H30 which has the highest values of Pav. For further investigation of the best configurations, Fig. 20 exhibits their load-deflection evolution. It is well-known that the non-linear behavior of these structures is provoked first by structural instability due to the nature of problem where the plastic deformation localizes in defined zones (plastic hinges). With the existence of hard zones, a coupling phenomenon is recognized leading locally to a strain state being complicated that orient the deformation mode and tube behavior. It is worth noting that the strain complexity occurs throughout the tube thickness directed by the interaction between the hard and the soft phase. With numerical simulations conducted by finite elements method as in [42], an overview on the strain and stress states throughout the tube thickness for each configuration is necessary to understand the local deformation scenario. Afterward, the total axial deflection of 50 mm is subdivided into five equally distance stages (i.e., 10 mm for each stage). Then, tubes responses for these stages were plotted in Fig. 21. The mean loads were calculated and presented via histograms set inside each figure. They provide a useful assessment of the local mean loads and their dependence on the case-hardening configuration. In the first stage, Fig. 21a reveals the highest local mean load for 3H30; whereas, it concerns 3R in the second stage (Fig. 21b) and it returns to 3H30 in the 3rd stage (Fig. 21c). The 3R case retakes the lead in the 4th stage. When the crushing process terminates in the 5th stage, 3H30 has again the highest local mean load. Hence, for these two cases (3H30 and 3R), their competition seems to be directed by complicated local strain induced by the metal like-composite tube, where a triaxial strain state was encouraged especially within the tube wall of 3H30. For this reason, the collapse load becomes function of case-hardened forms (Fig. 21). In order to evaluate and above all to quantify the effect of the local strain complexity within the tube wall occurring by these case-hardened forms, the proposed approach was based on a simple analysis

5. Concluded remarks A patented work [1] of energy dissipating system based on plastic buckling was used in this work. The concept consists of enhancing the energy absorbing capacity of thin-walled right-circular cylindrical mild steel tubes loaded axially. Based on the importance of the geometrical parameters of tubular structures η and λ, in directing the tube behavior, these two parameters were fixed throughout this study by η = 14.5 and λ = 0.18. Several case-hardened forms were designed, made and tested. They were four ring forms of 2, 3, 4 and 5 rings, two vertical strip forms (2 and 3 strips) and, six helical strip forms with three tilt angles of 30°, 45° and 60° (2H30, 3H30, 2H45, 3H45, 2H60 and 3H60). It should be noted that only 15% of tubes outer surface was case-hardened up to a certain depth of 0.5 mm for these distinct shapes. The produced specimen was so-called steel like-composite. The behavior of the crushed tubes demonstrates the dependence of the plastic buckling behavior on the composite type. The responses of these tubes didn't show a sensitivity to the used quasi-static strain rates. According to the recorded gain percentage, the effect of the casehardened forms was classified in three categories (low gain: 2R, 2H45 & 5R; intermediate gain: 3V, 2H60, 4R, 2H30, 2V, 3H60 & 3H45; and high gain: 3R & 3H30). It is concluded that such solutions, especially in the high gain category, provide more capacity in the energy absorption (i.e., mean collapse load). The maximum recorded gain in energy absorbed is up to 46% for 3H30. The material behavior seems to be directed by a complicated local strain induced by the metal likecomposite tube particularly in this category, where a triaxial strain state (compression, bending and shear strains). For this reason, the collapse load is dependent on hardened forms. References [1] A. Abdul-Latif, Metallic-Metallic Composite for a Plastically Deformable Member, INPI, (National Institute of Industrial Property), No. BT 890/1400843, 2014. [2] W. Johnson, S.R. Reid, Update to “metallic energy dissipating systems, Appl. Mech. Rev. 31 (1986) 277–288 (1978); Appl. Mech. Update 1986, pp. 315–319. [3] W. Abramowicz, N. Jones, Dynamic axial crushing of square tubes, Int. J. Impact Eng. 2 (1986) 179–208. [4] N. Jones, Structural Impact, Cambridge University Press, Cambridge, UK, 1989. [5] A.A.A. Alghamdi, Collapsible impact energy absorbers: an overview, Thin Walled Struct. 39 (2001) 189–213. [6] X.M. Qiu, T.X. Yu, Some topics in recent advances and applications of structural impact dynamics, Appl. Mech. Rev. 65 (2012) (024001-024001). [7] D. Karagiozova, N. Jones, Dynamic elastic-plastic buckling of circular cylindrical shells under axial impact, Int. J. Solids Struct. 37 (2000) 2005–2034. [8] D. Karagiozova, N. Jones, Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact, Thin-Walled Struct. 39 (2001) 583–610.

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