Plastic Collapse Stress Research Articles

A closed-form structural stress-strain relation and implications on plastic design limits in codes and standards

The deformation of elastic-perfectly plastic beam or plate under combined through-thickness membrane and bending stresses (i.e., structural stress) is analyzed in this paper. Closed-form solutions of “plane-remains-plane” strain (i.e., structural strain) distribution as a function of applied stress and yield strength is derived. The relationship between structural stress and structural strain is also revealed for gaining insights on not only the plastic collapse conditions, but also through-thickness deformation behaviors leading to limit state. Based on the closed-form strain solutions, four deformation modes are identified: (1) elastic, (2) one-side yielding, (3) two-side yielding, and (4) plastic collapse. A membrane-bending stress interaction diagram is constructed to depict four zones that are associated with the four deformation modes in the normalized membrane and bending stress space. Closed-form solutions of residual stress, residual strain, and structural stress range-strain range relation after a loading-unloading cycle are also derived. Based on the parabolic plastic collapse stress limit curve, parabolic design stress limit curves with coherent safety margins for any combinations of membrane and bending stresses are constructed. The new insights gained in this study offer a more consistent definition of design stress limit than those used in the current codes and standards, e.g., ASME BP&V Code.

Effect of co on mechanical and electrochemical properties of powder synthesized cellular Ti-Al alloy

ABSTRACT This work describes the effect of Co content on the compressive and electrochemical behaviour of cellular Ti4AlxCo (x = 2%, 4%, 6% and 8 wt%) alloy. Cellular products were prepared through powder metallurgy route by adding 70 v% of ammonium bicarbonate as space holder in Ti4AlxCo powder mixture. Relative density of the final products slightly upsurged due to increment of Co amount and it was found in the range of 0.32–0.35. Microstructure represented the interconnecting pores which will be advantageous to circulate the body fluid, if used as a bone implant. Plastic collapse stress of Ti4Al8Co was about 45% higher than Ti4Al2Co. Also, the elastic modulus was under the range of modulus of natural bone (11 ± 1 GPa). In Tafel plot, value of corrosion current density shifted from 8 μA/cm2 to 15 μA/cm2 by increasing the Co content from 2 wt% to 8 wt% which indicates the hampering of corrosion resistance. Corrosion rate followed the linear relationship with Co content. Best fitted electrochemical circuit showed the double layer oxide formation during corrosion. Micrographs of corroded cellular samples also represent that the surface of material is more prone to corrosion containing higher amount of Co.

Load-rate effects on the in-plane compressive behaviour of additively manufactured steel 316L honeycomb structures

Additive manufacturing (AM) offers the opportunity to enhance the mechanical performance of metallic honeycomb structures. However, there is limited research on the load-rate effects affecting in-plane compression. For the first time, this study investigates the in-plane compressive performance of Steel 316L honeycomb structures produced via material extrusion (ME) and laser powder bed fusion (LPBF). ME honeycombs of three cell sizes and single-cell size LPBF honeycombs were tested under uniaxial compression at varying quasi-static loading rates. Digital image correlation (DIC) was also employed to capture the deformation modes of the honeycombs and to map the local strain fields during compression. Empirical models were used to predict the in-plane compressive performance of the honeycomb structures. Particularly for the plastic collapse stress, an empirical formula incorporating viscoplastic dependency on the cell wall material within the quasi-static loading regime has been derived, producing accurate predictions. Both types of honeycomb structures are load-rate sensitive, as their compressive mechanical properties improved with the load rate increase. Moreover, the variation of the cell size was found to optimise the in-plane compressive performance. The deformation mode for both honeycomb structures was confirmed to be cell wall bending, plastic buckling, cell wall collapse, and folding.

Mechanical performance of bio-inspired hierarchical honeycomb metamaterials

Natural materials with hierarchical structures usually have superior mechanical properties. Herein, inspired by the macro–micro coupling deformation characteristics of biomaterials, novel hierarchical auxetic-hexagonal honeycombs (AuxHex) metamaterials with various substructures, including equilateral triangles and double arrowheads lattice cells, were constructed. A universal analysis model of the plastic collapse stress was first established, considering the deformation behavior of both the primary and secondary structures. This mechanism-based method gets rid of redundant numerical fitting parameters, and is applicable to different hierarchical lattice structures. Typical hierarchical AuxHex specimens were prepared using selected laser melting and stainless steel. In-plane compression tests and finite element simulation results demonstrated that, in contrast to the regular structures, hierarchical honeycombs exhibit enhancement in their load-bearing capacities and energy absorption ability. The specific modulus of T-AuxHex and A-AuxHex were increased by about 180% and 45%, the specific strength rose by approximately 50% and 15%, and the specific energy absorption was improved by about 160% and 50%. The effects of geometrical parameters were systematically discussed to reveal the mechanisms underlying the enhancement of the above mechanical characteristics. The proposed theoretical model provides a new method for designing the mechanical properties of hierarchical metamaterials by tailoring the type and distribution of secondary structures.

A lightweight rotationally arranged auxetic structure with excellent energy absorption performance

As one of the representatives of advanced lightweight cellular materials, the auxetic structure has a great potential for energy absorption due to its unique deformation mechanism, which makes a very promising application prospect in the fields of aerospace, vehicle and engineering protection. In order to further increase the energy absorption capacity of auxetic structures, this paper designed and characterized a novel two-dimensional (2D) lightweight rotationally arranged auxetic structure. The elastic properties, plastic collapse stress and specific energy absorption (SEA) of the novel auxetic structure were systematically investigated through theoretical calculations, numerical simulations and experimental method. Our results verify that the proposed theoretical model is accurate and applicable. The rotationally arranged shape and stable triangular design inside unit cells lead to an excellent energy absorption capacity, which is significantly higher than that of conventional auxetic structures (star-shaped honeycombs and re-entrant hexagonal honeycombs). Moreover, the SEA of novel structure has extremum conditions, by which the optimal relative density can be determined. According to different user requirements, the novel structure can be designed as the best energy absorption type or the most concise and lightweight type by adjusting geometrical parameters.

Plastic collapse model and drop-weight test of aluminum honeycomb under the out-of-plane compression

Firstly, according to the two dimensionless parameters proposed, the collapse stress factor and the hinge length factor, the unified expressions of the plastic collapse stress and the plastic hinge length are obtained from three theoretical formulas for honeycomb under the out-of-plane compression, which are the semi empirical formula, the Tresca yield criterion formula and the Mises yield criterion formula. Then, the different aluminum honeycombs are used in the out-of-plane compression to obtain load-displacement curves, stress-strain curves, and the energy absorption characteristics. Comparing the plastic collapse stress and the plastic hinge length of the measured values with those of theoretical values, they are found sometimes quite different. Finally, in order to reduce the differences between the measurement and the theory, the correction coefficient is introduced to establish the correction model of the plastic collapse stress and the plastic hinge length for honeycomb under the out-of-plane compression, which can provide new ideas for the selection and structural design of aluminum honeycomb.

Effect of ball powder ratio on microstructure and compressive behaviour of porous Ti-4wt %Al alloy

Ti and Al powders were milled in the weight proportion 24:1 using horizontal planetary ball mill. The ratio of ball to powder amounts (BPR) was varied (10, 15, and 20) in the milling process. Powder mixture milled with different BPRs were characterized by the XRD and FESEM to probe the evolution of phase and particles shape and size. Further, these mixtures were used to make porous cylindrical samples through space holder method. The used space holder amount was 60 v%. Compression test of the samples were performed on Universal Testing Machine. It was analysed that crystallite size, shape and size of the powder particles considerably affected by the used ball to powder ratio.XRD confirms that phase formation is invariant with the BPR. The observed relative density is about 10% higher than the used space holder content. Porous sample synthesized by the powder milled with 15 BPR has higher plastic collapse stress and energy absorption capacity as compared to the samples made of the powder milled with 10 and 20 BPRs.

Influences of relative density and strain rate on the mechanical properties of Al-cenosphere-SWNTs hybrid foams

In the present study, single-walled carbon nanotubes (SWNTs) and cenosphere reinforced closed cell hybrid aluminium foams (HAFs) of varying relative densities were produced, and their compressive deformation behaviour at different strain rates have been examined. The addition of SWNTs leads to a significant increase in plateau stress, plastic collapse stress, and energy absorption. This may be due to higher dislocation density and finer inter-SWNT spacing. The Raman spectra of HAFs showed the uniform distribution of SWNTs in the cell wall region. However, the effect of quasi-static strain rates (10−3 to 10 s−1) on the compressive deformation response is marginal. While the influences of higher strain rate ranges (10−3 to 1500 s−1) are considerably higher than the quasi-static strain rate range. The strain rate sensitivity of these foams is much less than unity (~0.0088-0.0314), indicating the brittle nature of foam deformation. The plastic collapse, plateau stress, and energy absorption of HAFs increase significantly with an increase in relative density. Interestingly, it is observed that both plateau stress and energy absorption follow power-law relation with relative density, and densification strain follows a linear relation with relative density irrespective of strain rate and foam material. It is further noted that the strain rate sensitivity of HAFs increases marginally with relative density. The deformation mechanism of HAFs has been examined using the digital photographs captured during the uniaxial compression test and the SEM, TEM images of deformed specimens.

Microstructure and mechanical behaviour of Ti-Cu foams synthesized via powder metallurgy technique

In the present study titanium based copper alloy foams were synthesized using acrawax as a space holder through powder metallurgy route. The effects of distinct pore size range and Cu content on the microstructural features, density, compressive and flexural behaviour was investigated. Results show that the amount of microporosity generated was more in case of foams with coarser pores than finer ones and also it increased with increase in Cu content. The presence of fine pores and lower amount of Cu led to generation of minimal amount of microporosity; resulting into greater relative density of Ti-Cu foams. The plastic collapse stress, plateau stress and bending strength of Ti-Cu foams decreased while densification strain increased with increase in Cu content. The maximum value of plastic collapse stress is reported for Ti-3Cu foam with fine pores. The plateau strength and bending strength of Ti-3Cu foam with fine pores was found to be higher than that of Pure Ti foams and was found to be the most optimized in terms of the characteristic features. The higher values of relative density, plateau and bending strength of Ti-3Cu foams makes them more preferable over pure Ti foams for implants applications.

Hybrid Auxetic Structures: Structural Optimization and Mechanical Characterization

With their increased energy absorption capacity, auxetic materials are perfectly fit to develop new, enhanced lightweight crash absorbers for cars. Herein, the mass distribution along the struts is optimized via finite element analysis with a parameterized optimization. Four different auxetic unit cells are taken from the literature and their struts parameterize, the models simulate, and the mass specific energy absorption capacity optimizes. The two models with the highest energy absorption capacity are then selected for experimental investigation and produced by additive manufacturing from a polymer. To further enhance the mechanical properties, the specimens are electrochemically coated with nickel and the polymer molten out by pyrolysis. Those Ni/polymer hybrids are subjected to quasistatic and dynamic impact experiments. Only a small strain rate sensitivity can be detected under dynamic loading, namely, a higher plastic collapse and higher plateau stress. The hollow struts are folding instead of bending, which render them much weaker than predicted by the simulation. In conclusion, it is possible to improve existing crash absorber elements with tailored auxetic hybrid structures. They absorb higher amounts of energy without changing their stiffness under dynamic loading while saving mass and cost.

Microstructural evolution, compressive deformation and corrosion behaviour of thermally oxidized porous Ti4Al4Co alloy made of mechanically alloyed powder

In the present work, porous Ti4Al4Co (0.56 ± 0.02 porosity) alloy samples were prepared through space holder technique using mechanically alloyed powder. Porous specimens having similar porosity were heat treated in open atmosphere at different heating time (10 h, 20 h and 30 h) to investigate the microstructural evolution, compressive deformation and corrosion behaviour. XRD and Raman analysis confirm the formation of oxide (layer) due to heat treatment. Microstructural analysis reveals the phase evolution in the sample due to thermal heating. Compressive stress-strain diagram indicates that plastic collapse stress and densification strain reduce with increment of heating time, but elastic modulus slightly increases. Icorr reduced significantly due to heating and it is 25 times lower for the 30 h heat treated sample than non-heat treated sample. In EIS curve, modulus of impedance and phase angle increase due to heat treatment which reveal that significant improvement in corrosion resistance occurs due to thermal heating.

Compressive deformation and corrosion behaviour of moderate to highly porous Ti4Al4Co (wt%) alloy foam

Porous Ti4Al4Co (wt%) alloy of different porosities were prepared through space holder technique. Effect of porosity on pore morphology, compressive deformation and corrosion behaviour of the foams were investigated. The prepared foams were characterized by XRD, FESEM and EDS to investigate the phase formation, pore morphology and elemental distribution. Compression test was performed to study the compressive deformation behaviour of the foams. Electrochemical and weight loss methods were used to investigate the corrosion behavior. From compression test, it was analyzed that plastic collapse stress, elastic modulus and energy absorption capacity reduce with the increment of porosity and follow the power law relationship. While, the densification strain increases linearly with porosity. On the other hand, increase in porosity imparts an adverse effect on the corrosion resistance of the material. The corrosion rate was found to be more susceptible to the foam samples having higher porosity. Microstructure of the corroded surface was in well accordance with the corrosion behaviour observed from the electrochemical method.

Failure bending stresses for pressurized pipes with circumferentially part-through cracks

Stress corrosion cracks detected in austenitic stainless pipes were circumferential cracks at inside of the pipes. Failure stresses for the cracked pipes were developed by net-section stress concept. Limit Load Criterion provided by the ASME Code based on the net-section stress concept can estimate fully plastic collapse stress, which is called as failure stress. Local Approach of Limit Load Criteria for estimating stress at crack penetration had developed for a part-through cracked pipe based on the Limit Load Criteria. Advanced Local Approach of Limit Load Criteria for estimating stress at crack penetration is newly developed based on the Local Approach in this paper. In comparing with experimental stresses of pipe crack penetrations, the Limit Load Criteria give un-conservative estimation, and the Local and the Advanced Local Approaches are close to the experimental stresses. In addition, the Advanced Local Approach always gives higher stresses than the Local Approach for internal cracks, and it is shown that the Advanced Local Approach is beneficial for thick wall pipes with large angle cracks.

Application Scope of Limit Load Criterion for Ductile Material Pipes With Circumferentially External Cracks

Abstract Bending stress at plastic collapse for a circumferentially cracked pipe is predicted by limit load criterion provided by the Appendix C of the ASME Code Section XI. The equation of the Appendix C is applicable for pipes with both external and internal surface cracks. On the other hand, the authors have developed a more precise equation taking into account the pipe mean radii at noncracked area and at cracked ligament area. From the comparison of Appendix C equation and the new equation, the plastic collapse stress estimated by the Appendix C equation gives about 20% less conservative bending capacity prediction for external cracked pipes with large crack angle and small Rm/t, where Rm is the pipe mean radius and t is the pipe wall thickness. This paper discusses the limitation scope to use the limit load criterion of the Appendix C equation.

Effect of SWCNTs content and relative density on the energy absorption capabilities of closed-cell Al-cenosphere-SWCNTs hybrid foam

Al-Cenosphere-SWCNTs closed cell hybrid foams (HFs) of varying relative densities (ρrd) were synthesized through stir casting technique using TiH2 (0.6 wt % of alloy) as a foaming agent, processed SWCNTs (0, 0.1, 0.2, 0.3 and 0.4 wt %) and cenosphere (4.25 wt % or 15 vol %) as thickening agent. Cenosphere particles provided micro-porosity within the cell wall and its shells act as reinforcement. It was noted that the addition of SWCNTs and Cenosphere improved the mechanical properties such as elastic modulus (Ef), plastic collapse stress (σpc), plateau stress (σpl) and, energy absorption capabilities (Eab) of HFs. In HFs these properties increases with increase in SWCNTs up to 0.3 wt % and a further increase in SWCNTs content leads to the reduction of these properties of HFs. It is interestingly observed that the densification strain (εD) for a constant ρrd is almost invariant to the SWCNTs content. The mechanical properties of the AFs and HFs foamsareempirically simulated and also compared with standard existing models for the different SWCNTs contents and ρrd. The deformation mechanism has been examined during compression test.

Positive, zero and negative Poisson’s ratio non-stochastic metallic cellular solids: Dependence between static and dynamic mechanical properties

Cellular solids are attractive materials due to their high specific static and dynamic mechanical properties. Even though these mechanical domains are interdependent, they are generally studied separately. This study uses a combination of additive manufacturing and vacuum assisted investment casting to manufacture low specific density (0.042–0.098) non-stochastic metallic cellular solids. An in-situ unitary cell geometric control is used to produce samples with positive, zero and negative Poisson’s ratios. The different values of this elastic constant allow the analysis of the distinct deformation in auxetic and non-auxetic behaviors. Deformation models are used to describe the static and dynamic behavior of the referred samples. It is shown that auxetic samples display higher values of apparent modulus and plastic collapse stress due to their densification effect. In terms of dynamic properties, samples with slightly negative and zero rib angles show higher values of damping. This is attributed to the more favorable flexure component of deformation and variations in material volume that influence the hysteretic damping. Overall, it is suggested that the most beneficial combination of specific density, static and dynamic mechanical properties is observed in samples with a rib angle of −10° and a Poisson’s ratio of −0.34.

Mechanical properties and energy absorption capability of AuxHex structure under in-plane compression: Theoretical and experimental studies

The architected mechanical metamaterials have garnered significant research attention for a variety of engineering application due to their remarkable mechanical properties and unique deformation behavior. Herein, the in-plane uniaxial compressive response and energy absorption capacity of a novel hybrid configuration, AuxHex structure, which consists of auxetic and hexagonal honeycomb cells, are systematically investigated through theoretical, finite element simulation and experimental methods. A series of AuxHex sandwich core panels have been fabricated with nylon material by using additive manufacturing route. The relationships for Young's modulus and plastic collapse stress along different loading directions are derived and validated through the comparative analysis. In addition, the deformation mechanism and failure modes of the AuxHex structure have also been discussed in detail. The AuxHex structures have exhibited superior Young's modulus, collapse strength and energy absorption than traditional honeycomb structures. In the x-direction, the energy absorption capacity was improved by 38%, which can be attributed to the uniform and stable deformation mode of the unit cell. The theoretical prediction results of Young's modulus and plastic collapse stress are consistent with finite element simulation and experimental results. The AuxHex structures demonstrate a novel design strategy for the architected metamaterials through the combination of various cellular cells. The hybrid structures will play an important role in both the load-bearing and energy-absorbing applications, and it demonstrates a novel design strategy for the architected metamaterials through the combination of various cellular cells.

Synergic effect of MWCNTs and SiC addition on microstructure and mechanical properties of closed-cell Al–SiC-MWCNTs HCFs

AlSi12Cu1Mg1–SiC-MWCNTs hybrid composite foam (HCFs) of varying relative densities (R.D.) were made through stir casting technique using CaH2 as a foaming agent. Varying wt.% of SiC and multi-wall carbon nanotubes (MWCNTs) were used as reinforcing as well as thickening agents. Uniform distribution of SiC and MWCNTs in the matrix was confirmed by FESEM images and Raman analysis. It was observed that the elastic modulus (E), plastic collapse stress (σpc), plateau stress (σpl), and energy absorption (Eab) of HCFs increase significantly when both (MWCNTs and SiC) were added together. But, when SiC and MWCNTs added individually, the extent of improvement in these properties is relatively low. However, densification strain varies marginally with the variation in reinforcement. Irrespective of reinforcement, the σpl, the E, and the Eab increased with increment in R.D. The different values also followed the existing relations, when the fraction of cell edge materials varied with R.D., the deformation mechanism was understood from photographs taken during deformation.

A comparative study on compressive deformation and corrosion behaviour of heat treated Ti4wt%Al foam of different porosity made of milled and unmilled powders

Ti4wt%Al alloy foams of various porosities were prepared using milled and unmilled powders through space holder technique. Crystallographic and morphological change in milled powder compared to the unmilled one were also examined. Space holder content was varied to get foams of different porosities. After sintering, foams were thermally oxidized through heat treatment and characterised in terms of their pore size, pore morphology, pore interconnectivity, phase formation and compressive deformation behaviour. It was observed that plastic collapse stress, elastic modulus, plateau stress and energy absorption capacity are strong function of porosity and these are higher for the foam made of milled powder (Mf) than those of the foam made of unmilled one (Uf). Corrosion behaviour of these foams were examined. Open circuit potential, Tafel plot and electrochemical impedance spectroscopy confirm that Mf has higher corrosion resistance than Uf for the same porosity level. Also, with increasing porosity, corrosion resistance of the foam samples reduces.

Influence of Cell Anisotropy and Relative Density on Compressive Deformation Responses of LM13-Cenosphere Hybrid Foam

This article deals with closed-cell aluminum alloy LM13-cenosphere hybrid foams (ACHFs) with cell anisotropy prepared through stir casing technique. The compressive deformation behavior of hybrid foams in both transverse and longitudinal directions was measured at a strain rate of 0.01/s. The hybrid foam loaded in longitudinal direction (LD) shows higher plastic collapse stress than that in transverse direction (TD). The stress drop ratio is also observed to be higher in the LD. The plastic collapse stress and energy absorption capacity of ACHFs follow the power law relationship with relative density in both the directions. The plateau stress is higher in case of LD and densification strains are marginally higher in case of LD than that in TD.