Static and dynamic crushing of novel porous crochet-sintered metal and its filled composite tube

A novel porous crochet-sintered metal (PCSM) is fabricated by rolling a crocheted porous cloth and subsequent vacuum sintering using a continual single super-fine soft 304 rope twisted by 49 fibers as raw material. This work investigates the quasi-static and dynamic axial crushing response of PCSMs and their filled composite tubes. The pore structures of PCSMs are formed by inter-crocheted and multiple inter-locked rope skeletons and metallurgical bonds. The PCSMs have almost no initial impact effects with a high crushing force efficiency. Filling the PCSMs changes the deformation model of 6063 tube, improves the static crashworthiness parameters of 6063 tube by 8-25% with almost no increasing initial impact effect, and doesn’t always play a positive role in dynamic absorption. Porosity has obvious influence on the quasi-static and dynamic behavior and crashworthiness of PCSMs and their filled composite tube, and the effect of porosity on dynamic crashworthiness of composite tube is greater than that on quasi-static crashworthiness of composite tube. The PCSMs and their composite tubes show great potential for application in energy absorbers. The method of filling PCSM into bare tube is possible to improve the energy absorption ability of thin-walled tube with almost no increase in the initial peak force.


Introduction
Thin-walled metal tubular structures for energy-absorbing components have demonstrated effectiveness of crashworthiness and have been extensively studied over the last few decades because of their smart and simple structure, superior rigidity, stable deformation, high energy absorption efficiency, good workability, and low cost [1][2][3][4]. Initial studies focused on the crashworthiness of different cross-and longitudinal-sectional shapes of thin-walled metal tubes.
Circular and square tubes are traditional energy-absorption components [5][6][7][8]. Then, the crashworthiness of polygonal tubes such as odd-sided tubes (triangular and pentagonal tubes [9,10]) and even-sided tubes (hexagonal and octagonal tubes [11], 12-sided and 16-sided star tubes [12]) were investigated [13,14]. In addition to these straight tubes, tapered and graded tubes [15,16] have also attracted research attention. All these tubes have distinctive features, and their sectional shapes greatly affect their energy absorption capacities. However, their initial peak force is high, which is not advantageous in anti-collision absorption applications.
The filled composite structure filled with lightweight materials such as aluminum foam, aluminum honeycomb and hollow metal spheres attracts considerable interests. Seitzberger et al. [31] carried out some experimental investigations to study the crushing behavior of different tubes and their composite structures filled with aluminium foam. The results showed that the foam can effectively improve the energy absorption of empty tube even if stoke lengths were reduced. Hanssen et al [32] studied the axial deformation behavior and energy absorption of AA6060 aluminium tubes filled with aluminium foam under both quasi-static and dynamic loading conditions by performing 96 tests. The foam improved the ability of energy absorption of bare tube. The inertia effects raised the load of bare tube during crushing. Song et al. [33] investigated the "interaction effect" between aluminum foam and metal column by experiments, numerical simulation and analytical models. The crushed foam filler could be further divided into two main energy-dissipation regions i.e., densified region and extremely densified region.
When filled with foam, energy absorption was found to be increased both in the hat section and the foam filler. Rajendran et al. [34] investigated the impact energy absorption characteristics of 304 stainless steel tube filled with closed cell aluminium foam. Foam filled tubes undergo less deformation in comparison with the individual foam or unfilled tube for absorbing the same amount of impact energy. Foam-tube may be a potential and more efficient energy absorber. As early as 1998, Santosa and Wierzbicki [35] studied the quasi-static axial crushing resistance of a square box column and its composite structure filled with aluminum honeycomb or foam. Aluminum honeycomb and foam filling improved the ability of energy absorption to a different degree. Aluminum honeycomb filling is more weight efficient than aluminum foam filling. Zarei et al. [36] investigated the Axial and oblique impact behavior and energy absorption on empty and honeycomb filled aluminum square tubes. Results have indicated that filling of tubes with honeycomb can improve the crashworthiness behavior. But when the density of honeycomb exceeded the critical density, the composite structure will lose its weight efficiency. Therefore, selection of honeycomb density was very important. Yin et al. [28] researched the energy absorption characteristics of honeycomb-filled single and bitubular polygonal tubes (HSBPT). The results showed that the crushing force of HSBPT was higher than that of the empty tube. The honeycomb-filled single tube was superior to the honeycombfilled bitubular tube. Wang et al. [37] aimed to research the detailed mechanical and energy absorption properties of honeycomb-filled thin-walled square tube (HFST) structures with different geometric configurations and matching relationships between inside honeycomb core and outside metallic thin-walled tubes. Results showed that the composite HFST structures may be rapidly gaining popularity as energy absorbers, since they significantly contribute to the energy absorption. Xin et al. [29] focused on the quasi-static axial crush performance of thin-walled tubes filled with hollow metal spheres (TWT-HMS) and their individual components under axial compressive loads. The results indicated that the hollow metal spheres could improve the axial bearing capability of bare tube, and the biggest improvement scale could be 300%, which is due to the superimposed effect. All these composite structures can improve the energy-absorbing capacity of thin-walled metal tubes. However, the initial peak load also increases significantly, which is not beneficial for structural crashworthiness. Under impact loading, a composite tube filled with a porous structure not only absorbs more energy, but also diffuses and weakens the stress waves, which is an effective method of improving the energy absorption of the tubes.
Another category of porous metal materials is porous metal fiber/wire materials with excellent energy absorption and crushing characteristics. This kind of porous material can avoid the brittleness and frailness of foam aluminum and does not break under large plastic deformation. Fiber/wire as a raw material offers several benefits, such as high strength, good toughness, minimal defects, and low cost. Further, wire-based products are well developed for various classical textile manufacturing processes. Porous metal fiber/wire materials such as porous sintered fiber/wire materials [38][39][40][41][42], entangled fiber/wire materials [43,44], and wirewoven cellular metals [45,46] [45]. At present, porous metal fiber/wire materials are prepared by short or medium-length metal fiber/wire. When short fibers/wires are used as raw materials to prepare porous metal fiber/wire materials, a mold should be fabricated first according to the geometric size of the required porous material. Then, green bodies are obtained by putting short fibers/wires into the mold to cold press. The porous metal short fiber/wire material is fabricated after placing the green bodies in a vacuum furnace to sinter. The porous structures of this type of porous material are not uniform and controllable because of the short fiber/wire random overlapping. The cost of short fibers/wires is high. When the porous material has a different geometry, the mode also needs to be processed again. When medium-length fibers/wires are used as raw materials to prepare porous metal fiber/wire materials, the medium-length fibers/wires should be preprocessed into spiral shapes and then placed into a prepared mold to cold press. Finally, porous materials can be directly formed, such as metal rubber, or formed after sintering. Compared to the porous metal short fiber/wire material, the porous structures of this type of porous material are uniform and controllable. However, a mold is still needed.
Wire-woven metals are a type of cellular metal composed of uniform 3D truss-like cells. This kind of porous material needs a special weaving machine, although it does not need a mold.
The porous structure of this type of porous material is regular and controllable. However, the complex and expensive weaving equipment leads to high cost for wire-woven metals.
Although many studies have shown that porous metal fiber/wire materials exhibit good energy absorption properties and a large plastic deformation capacity, there are no investigations on the crashworthiness of thin-walled metal tubes filled with this kind of lightweight porous material with high energy absorption capability. In this study, we adopted a new method to prepare novel porous metal wire materials, i.e., porous crochet-sintered metals (PCSMs), and then filled them into 6063 thin-walled tubes to form a new type of composite structure. The crashworthiness of the composite tubes filled with PCSMs with different porosities under compressive loading were investigated. It is expected that this work will demonstrate a valuable method of providing a new filler for preparing composite tubes to improve the crashworthiness of thin-walled metal tubes.

Specimen preparation
The filled composite tubes were formed by novel porous crochet-sintered metals and 6063 aluminum alloy thin-walled tubes.
PCSMs were fabricated by sintering crocheted super-fine soft stainless steel wire rope. In this study, 0.5-mm-diameter 304 steel wire rope twisted with 49 steel wires was used. The PCSMs were processed by crocheting and vacuum sintering. Pull the steel wire rope through the loop. # Pick up the steel wire rope again. Pull through the loop on the hook *. Repeat from # to *, until ten chain stitches are completed in the porous crocheted metal, as shown in Fig. 1a.
Crochet the first row: Insert the hook under the V of the second chain (Fig. 1b). Pick up the steel wire rope. Pull the steel wire rope through the hook (Fig. 1c). There are two loops on the hook. Pick up the steel wire rope and then pull it through the two loops on the hook (Fig. 1d).
A single crochet is completed (Fig. 1e). # Pass the hook through the next chain stitch, and then pick up the steel wire rope and pull through the chain stitch. Pick up the steel wire rope and pull through the two loops on the hook. Another single crochet is completed *. Repeat from # to *, until the first row is completed (Fig. 1f).
Crochet the second row: # Turn the work around to begin the second row (Fig. 1g). Insert the hook through the next stitch and pick up the steel wire rope (Fig. 1h). Then, pull it through the stitch. Pick up the steel wire rope again. Pull it through both loops on the hook. The second single crochet is completed *. Repeat from # to * until the second row is completed (Fig. 1i).
The procedure was repeated according to the method of crocheting the second row until the porous crocheted cloth was completed (Fig. 1j). It was rolled into a cylinder (Fig. 1k) and then inserted into the corundum tube (CT), as shown in Fig. 1l. Then, they were placed in a vacuum furnace (WHS-20 vacuum sintering furnace) to sinter at 1300 °C for 150 min. The heating rate was maintained at 10 °C min −1 when the temperature was below 800 °C, and 75 min was required for the temperature to increase from 800 °C to 1330 °C (Fig. 1m). The samples were cooled to room temperature inside the furnace chamber. During sintering, the vacuum pressure was maintained at approximately 1×10 −2 Pa until the temperature dropped to 200 °C. The novel porous crochet-sintered metal was complete when it was pulled out from the CT (Fig. 1n). The filled composite tubes were made by inserting the porous crochet-sintered metal into 6063 thin-walled tubes without any adhesive. The matching process is shown in Fig.   2. The total mass of tup is 19.739 kg, which includes tup holder mass (6.175 kg), additional mass (10.500 kg) and tup nominal mass (3.064 kg). The falling height of impact plate is 1835 mm which means that the initial impact velocity is about 6.00 m/s. The initial kinetic energy is approximate 354.96 J. The density was determined by the hydrostatic weighing method, according to the Archimedes theory. The average porosities of the PCSMs can be expressed as the following equation [28,36]: where P is the average porosity, D is the density of the PCSM, and  is the density of the 304 steel wire (7.93 g/cm 3 ).  shows the appearance and metallurgical bonding of PCSM. Owing to its fabrication by the special method described in Section 2, the spatial structure of the PCSMs is quite different from that of entangled wire materials (quasi-ordered [43] or random [44]) or wire meshes [39]. The PCSM macrostructure exhibits an inter-crocheted and multiple interlocked rope mesh structure ( Fig. 3a and b). The rope skeleton is made of seven strands of ropes twisted into a single rope (a strand of rope is twisted by 7 wires). There are abundant metallurgical bonds not only along the twist direction of the wires but also at the contact position between rope skeletons.   The quasi-static load-displacement curves of the PCSMs exhibit obvious elastic-plastic behaviors similar to those of other porous fiber/wire metals [47], such as entangled fiber/wire materials [43,44], wire-woven cellular metals [45,46,48], and fiber networks [42,49,38].

Crushing curves of repeated tests
Namely, they exhibit three typical deformation stages (Fig. 6a), i.e., a transient elastic stage, a long and smooth quasi-platform stage with plastic collapse, and a final densification stage with a sharp stress increase. Unlike metallic solids, which exhibit distinct yielding points, the PCSMs do not show a distinct yielding point because of the elastic stage transiting smoothly to the plastic platform. We define the crossing point of the extension of the elastic curve and quasi-platform curve as the yielding point [43], as shown in Fig. 6a. As expected, the yield load decreases as the porosity increases. The PCSMs present a smooth and slanted loaddisplacement platform; this is different from aluminum foam or honeycomb, which show a large and flat plastic platform with jagged fluctuation. We call this stage "pseudo-platform", borrowing from a reference [43]. It is found that the pseudo-platform of the PCSM1, with approximate 85% porosity, became shorter and less obvious than that of the PCSM3 with approximate 89% porosity. Noticeably, the curve-slope of the pseudo-platform increases as the porosity decreases. The PCSM with small porosity exhibits a large curve-slope, i.e., the pseudoplatform deviates from the normal platform. The PCSM with large porosity corresponds to the small curve-slope like a platform. The dynamic load-displacement curves of PCSMs go straight into a plastic platform stage, then enter into the densification phase, and get into the last unloading stage (Fig. 6b). There is no elastic stage of the static curve for the dynamic curve.
Under the same impact condition, the PCSM33 with about 89% porosity has the highest impact load (81 kN) than that of PCSM23 with approximate 88% (76 kN) and PCSM13 with approximate 85% (67 kN). It indicates that the PCSM13 with lower porosity has better ability to resist impact load than the impact resistance of the other PCSMs with higher porosity.
Porosity has obvious influence on the dynamic behavior of PCSMS. The porosity of PCSM23 differs by about 1% from that of PCSM33, and the dynamic load-displacement curve of PCSM23 almost coincides with that of PCSM33, but in fact, the impact load of PCSM33 is about 6% lower than that of PCSM23. The porosity of PCSM13 is only 3-4% higher than that of the first two. However, there is an obvious gap between the dynamic load-displacement curve of PCSM13 and those of PCSM13 and PCSM23, and the impact load of PCSM13 is appropriate 21% lower than that of PCSM23. The effect of porosity on dynamic compressive curve is same as that on static compressive curve. For 6063 thin-walled tubes, both static curve and dynamic curve present obvious initial peaks. The dynamic initial peak (near to 46 kN) is about twice as high as the static initial peak (approximate to 24 kN). The static curve shows three typical deformation stages (Fig. 6c). The dynamic curve only exhibits the elastic stage and plastic platform stage (Fig. 6d).   (Fig. 8a). Although there is no dynamic crushing process, it is easy to understand that the dynamic crushing process of PCSM is also a process densification with the pore structure disappearing rapidly, which is similar deformation process as the static crushing process of PCSM. In order to more clearly represent the category to which the test samples belongs, the "tube+PCSM1", "tube+PCSM2" and "tube+PCSM3" coded words will present the "tube+PCSM17", "tube+PCSM27" and "tube+PCSM36" in Fig.5c, respectively. Fig. 10a-10d show the static load-displacement curves of filled composite tubes with different-porosity PCSMs. Their deformation stages are similar to that of the thin-walled tube, i.e., pre-crushing with a linear elastic zone, post-crushing plastic stage with folds forming, and a compact zone with load increasing sharply. The PCSM load-carrying capacity is extremely small, so the sum of the load of a single tube and PCSM is fairly close to that of the bare tube. For the filled composite tube with approximately 85% porosity (PCSM1), compared with the bare tube and the sum of the two components (Fig. 10a), the initial peak force is almost unchanged; the average load-carrying capacity shows an obvious increase (the curve of the composite tube is at a higher position than that of the bare tube and the sum of the two components). The wave crests have become more obvious and moved forward or backward in location. The width of the waves decreases. It is known that the fluctuating state of the curve in the post-crushing stage is directly related to the forming process of the folds. Every fold forms during the crushing process of the filled composite tube, leading to the generation of a sawtooth wave on the load-displacement curve. The number of folds corresponds to the number of peaks within the compression stroke. Fig. 11a and Fig. 12a show the crushing process and failed specimens of the filled composite tubes with PCSM1. The crushing deformation of the composite tube proceeds in ring mode starting at the distal end, which is quite different from that of the bare tube in diamond mode (Fig. 9a). The failed specimen (Fig. 12a)   This position yields first, which results in starting the crush deformation from the lower part of the composite tube with PCSM1 (Fig. 11a). Fig. 12b shows the thin structure approximately in the center of the composite tube with PCSM2. This position yields easily, which leads to a crushing process from the middle part of the composite tube with PCSM2 (Fig. 11b). Fig. 12c shows the looser rope mesh structure at the top of the composite tube with PCSM3. This position yields first, so the crushing process starts from the top part of the composite tube with PCSM3 (Fig. 11c). There do not appear any fractures like those observed with aluminum foam filler under large plastic deformation, and the PCSMs are still continuous integral structures.
This feature is advantageous to its application.
All phenomena indicate that filling PCSMs into the thin-walled tubes can improve the loadcarrying capacity without increasing the initial peak force and can change the deformation mode from diamond mode to ring mode. There is not only an obvious composite effect, but also an interaction effect between the two components.  The effective stroke ratio (ESR) is the ratio of the ES to the total length (L) of the PCSM, which is similar to the "densification strain" of cellular materials or porous metal fiber/wire materials.
The definition of ESR avoids the subjective random energy absorption evaluation and provides a unifying base for evaluating the effective utilization rate of tubular structures.
The above method of obtaining effective stroke and its ratio is only applicable to the quasistatic crushing deformation and the dynamic crushing deformation without fracturing for tubes.
In this work, we use the formulas (2) and (3) to calculate the ES and ESR of tubes for the quasistatic crushing deformation. For the low velocity impact deformation, the displacement at the end of each impact stroke is the effective stroke of tube.
The energy absorption values of all tubes increase linearly ( Fig. 14a and 14b) until the end of compression. However, their deformation efficiency first increases and then decreases. The change trend of PCSMs is approximately linear, whereas that of the 6063 tube and filled composite tubes present fluctuations (Fig. 14c). Peak values appear in the deformation efficiency curves. In Section 3.2, we know that not only PCSMs but also 6063 tube or composite tubes all experience the densification or compact stage with load sharply increasing in the last crushing. The force F in Eq. (2) far exceeded the compression plateau force and increased continuously, whereas the displacement increment decreased. Thus, the deformation efficiency has a maximum value. The compression displacement corresponding to the maximum value is the most effective energy absorption length of the tubular structures. The ESR can be calculated by Eq. (3). Fig. 13c shows that the ES of the PCSMs is somewhat shorter than that of other tubes. The bare 6063 tube has the greatest ESR, approximately 0.68. The ESRs of PCSM1, PCSM2, and PCSM3 are 0.58, 0.62 and 0.61, respectively (Table 2). After filling PCSMs into the bare 6063 tubes, the ESRs of the composite tubes are approximate 0.65, which is slightly less than that of bare tube and more than those of the PCSMs.  phenomenon can be still detected, that is, a longer compression stroke is required to absorb the same amount of energy for PCSM with low porosity. The amount of energy absorbed per unit length for PCSM with low porosity is low. This feature is found not only in dynamic absorption but also in static energy absorption. Of course, when the PCSM is filled into the 6063 tube, the composite tube filled with PCSM33 (Tube-PCSM33) will need a longer stroke to absorb 350 J impact energy than the other two, i.e., Tube-PCSM23 and Tube-PCSM13. And all composite tubes experience shorter strokes than those of PCSMs to achieve a similar amount of energy absorption. However, the 6063 tube has a shorter stroke than that of the PCSM23 and PCSM33, which indicates that filling the PCSM into alone tube does not always improve the dynamic energy absorption capacity of 6063 tube. Fig. 15 shows the dynamic energy absorptiondisplacement curves of all tubes and PCSMs for absorbing approximate 350 J impact energy.
It clearly shows the relationship of effective strokes among various structures in order to absorbing the similar amount of energy.
The crushing force efficiency (CFE) is the ratio of the mean crushing force to the initial peak force [15,16], as The CFE is a parameter to evaluate the uniformity of the crushing force. A lower CFE means that the initial impact effect on the structure is too obvious, which is not good for protective structures. A higher CFE means better structural crashworthiness. and CFEs all decrease with increasing porosity. All the PCSMs have very small initial peak forces. Further, the mean crushing forces are somewhat higher than their initial peak forces.
This feature is good for structural crashworthiness and shows that there is no initial impact effect, which indicates that the PCSMs will enter directly into the energy-absorbing platform stage. The CFE values of PCSMs are higher than those of aluminum foam with high crushing force efficiency, mainly in the range of 0.8-1.0 [26], and approximately 3 times that of aluminum honeycomb (0.4-0.5) [26]. The PCSMs may fully utilize their energy absorption capacity, as do aluminum foam and honeycomb, and satisfy the low peak load requirement for energy absorbers.  Table 2.
The 6063 thin-walled tube presents a large initial peak force (23.57 kN) during the crushing process; it is much higher than the mean compression force (15.35 kN), as shown in Fig. 4b.
This is a drawback for fully dense thin-walled metal tubes that cannot be ignored. The higher initial peak force may cause destruction of the object before the tube can play the role of buffer by absorbing energy. Hence, it is important to reduce or control the initial peak load of the energy absorbing structure. The consistency of the initial peak force and the mean crushing force (CFE) is highly important for structural crashworthiness. A greater CFE means lower initial impact, which is beneficial for structural protection.
After matching the thin-walled tubes with the PCSMs, the initial peak forces of filled compared to that of bare tube (0.65). These results imply that the PCSMs can improve the crashworthiness of bare tube almost without increasing the initial impact effect. Fig. 12 shows that the mean crushing force and CFE obviously decrease, and the initial peak force is almost the same with increasing porosity.  Table 3. The above three parameters of TP23 and PT33 are lower than those of bare tube except that of TP13. The mean crushing force and CFE of TP13 increase 20% and 16%, respectively, while the initial peak force only increases by 2.7%. It indicates that the method of filling PCSM into bare tube is possible to improve the energy absorption ability of thin-walled tube with almost no increase in the initial peak force. (1) The PCSM preparation method is simple and low-cost because there is no need for a special mold for cold pressing or special high-cost weaving equipment. The raw material was continuous single rope, which need not be cut into segments or predeformed. The macrostructure of lightweight PCSMs were characterized by their inter-crocheted and multiple interlocked porous structure, rope skeletons, and metallurgical bonds.
(2) The quasi-static load-displacement curves of PCSMs exhibited three typical deformation stages while their dynamic load-displacement curves go straight into a plastic platform stage. There were almost no initial impact effects. The porosity of PCSM1 decreased only by approximately 4.5 percent compared with that of PCSM3. The mean crushing force and effective energy absorption of PCSM1 for static tests increased by approximately 60% and 52%, respectively compared with those of PCSM3. The mean crushing force and impact load of the former increased by 6% and decreased by 17% than those of the later. Porosity has obvious influence on the quasi-static and dynamic behavior and crashworthiness of PCSMS. The quasi-static and dynamic crushing deformation of PCSM all exhibited the densification process with coupling structural plastic deformation and rope framework plastic deformation. porosity only increased by approximately 10%, 7% and 7% than those of filled with PCSM with 89% porosity, respectively. But the dynamic values of Pmean and CFE of the former is higher 51% and 46% than those of the latter, respectively. The effect of porosity on dynamic crashworthiness of composite tube is greater obvious than that on quasi-static crashworthiness of composite tube.