Strain Hardening Effect Research Articles

Impacts of the alloying elements and thermo-mechanical processing on the phase stability, crystalline structure, microstructure, and selected mechanical properties of Ti-(10-x)Al-xV (x = 0, 2, and 4 wt%) alloys targeted as external prostheses

This study aimed to characterize Ti-Al-V alloys submitted to thermo-mechanical processes and evaluate their impact on the crystalline structure, microstructure, coefficient of thermal expansion (CTE), selected mechanical properties, and cytotoxicity. X-ray diffraction (XRD) analysis revealed a major α phase, with V acting as a β-stabilizer. The cooling rate and the plastic deformation contributed to the formation of minor martensitic α′ and β phases, with notable variations in cell parameters. The Energy-Dispersive XRD indicated the CTE was dependent on the alloying elements. Ti-10Al and Ti-8Al-2V depicted Widmanstätten laths and basket-weave structures, while Ti-6Al-4V showed typical features of β grain boundaries. Thermodynamic predictions aligned with the observed phase compositions. Vickers micro-hardness tests yielded values surpassing those of commercially pure titanium (CP-Ti), attributed to the synergistic effects of solid solution, phase precipitation, and strain hardening effects. And, elastic modulus approximated that of CP-Ti, largely due to the α phase's predominance. The solution treatment reduced the elastic modulus compared to the hot-rolled samples due to the stress relief and α′ and β phase precipitation. Preliminary cytotoxicity assays confirmed the non-toxicity of the samples to cell viability. These findings suggest that the solutionized Ti-10Al sample is an economically viable candidate for fabricating external prostheses.

Improving strength-ductility synergy of titanium matrix composites containing nitrogen via the introduction of intragranular nano-TiB

We prepared a titanium matrix composite (TMC) with added boron nitride nanosheets (BNNSs) for strength-ductility trade-off issues. The composite, characterized by in-situ nano-TiB intragranular distribution and trace nitrogen solid solution, was prepared using rapid hot press sintering (FHP) and short-duration hot rolling. During pre-rolling heat preservation, the diffusion of boron and nitrogen resulted in the intragranular distribution of nano-TiB and nitrogen solid solution. The nano-TiB demonstrated excellent load transfer, fracture suppression, and dislocation storage capabilities at both room and high temperatures. Coupled with the nitrogen solid solution, the composite exhibited a significant enhancement in strain hardening effect compared to the titanium matrix. The composite outperformed the titanium matrix in strength and ductility at both room and high temperatures, demonstrating a notable strength-ductility synergy. This work provides a reference for designing TMCs with excellent performance at both room and high temperatures.

Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames

In eccentrically braced frames (EBFs), inelastic behavior is only permitted in the links. All members, except for the links, are designed according to the capacity design concept by using the link overstrength factor, Ω, so that they remain elastic even when the links develop their ultimate strength (including the strain-hardening effect). AISC 341 specifies that the Ω factor of link members must be 1.25 for beam and brace design and 1.1 for column design. In this study, the relevance of the current Ω factor was investigated. A total of 471 K-braced EBF systems with various conditions were designed using a multi-objective optimization technique, and nonlinear dynamic analyses were performed to evaluate the Ω factor. The results indicate that it is reasonable to use the current Ω factor for the design of beam outside link and brace; however, it leads to an overestimation of axial force in columns, especially in the lower stories of tall buildings. From the analysis results, a new Ω factor equation for column design was proposed. It was demonstrated that the structural quantities of 15-story frames designed using the proposed equation decreased by an average of 19% compared to those designed using the current Ω factor.

Elastoplastic plate shakes down under repeated impulsive loadings

When subjected to repeated dynamic impacts at identical load level, a metallic monolithic beam/plate may reach a stable state wherein measurable deformation ceases (i.e., shakedown in elastic state) after undergoing a sequence of elastoplastic deformations, which has been termed as “pseudo-shakedown” (P-S) (Jones, 1973; Shen and Jones, 1992). While the response of a single beam/plate under repeated low-velocity impacts has been thoroughly studied, its dynamic behavior under high-velocity impacts, such as explosive or alternating impulsive loads, is difficult to measure experimentally, due mainly to high costs and setup challenges. In the current study, the method of metallic foam projectile impact was employed to produce repeated impulsive loadings on a fully-clamped elastoplastic monolithic plate made of L907A (a Chinese standard shipbuilding steel). Its dynamic responses, including mid-point deflection versus time histories, final deflections, and deformation modes after each impact, were systematically measured. The phenomenon of dynamic shakedown was observed. To further explore this phenomenon, the method of finite elements (FE) was employed to simulate the repeated impulsive impact test, and its prediction accuracy was validated against experimental results. Unlike an elastoplastic (e.g., steel) monolithic plate subjected to repeated low-velocity impacts, which exhibits zero plastic energy dissipation in the P-S (pseudo-shakedown) state, the same plate under repeated high-velocity impacts shows a small level of plastic energy dissipation in the P-S state, mainly due to more extreme loading conditions. The initial impact momentum, yield strength, and tangent modulus of the material the plate is made of significantly affect both the stable deflection in the P-S state and the number of impacts needed to reach it, while the elastic modulus has limited influence. A modified dimensionless impulse loading number, accounting for the strain-hardening effect, is proposed. An approximately linear relationship between stable deflection in the P-S state and impulsive loading is found in dimensionless form.

Growth of thermoplastic shear band

Shear localization is a fundamental and widely observed non-equilibrium phenomenon in metallic materials subjected to impulsive loadings. Despite extensive research over several decades, the evolution of shear bands still remains poorly understood. In this study, we propose a two-stage model to describe the evolution of thermoplastic shear band, where the effects of strain hardening, strain-rate hardening, and thermal softening are involved. Our analysis reveals that the growth of thermoplastic shear band is derived by the competition between momentum diffusion and thermal diffusion processes, which is controlled by the solid-state equivalent of the Prandtl number. By incorporating these factors into our model, we find that the presence of hardening effect retards the evolution of shear bands, resulting in a wider shear band and increased dissipation of energy. Theoretical calculation results of shear bandwidth, shear band strain, propagation velocity, process zone geometry and dimensions, critical dissipation energy, shear band toughness, and shear band spacing are well consistent with available experimental data. Additionally, we explore the potential transition to turbulence controlled by Reynolds number within shear bands and investigate the influence of the Taylor-Quinney coefficient on the evolution of shear bands. These findings are expected to offer valuable insights into the mechanism of shear band evolution.

A new plastic global analysis approach for the fire design of steel and stainless steel structures

The new generation of structural codes for stainless steel allow carrying out global plastic analyses on certain types of stainless steel structures with plastic cross-sections at room temperature if the joints conforming the structure are classified as full-strength joints, a capability that has been long recognised for carbon steel structures. However, the requirements for the fire design of carbon and stainless steel structures in current and upcoming European design standards are still primarily based on the resistance of individual members, disregarding the redistribution of internal forces and strain hardening effects. Recent studies have proven that carbon and stainless steel frames with plastic cross-sections and full-strength joints are capable of redistributing internal forces at elevated temperatures, and failed describing global plastic collapse mechanisms under fire situation, suggesting that system effects are also relevant at elevated temperatures and could be taken into account for more efficient designs. On this basis, this paper develops an extensive numerical study focused on carbon and stainless steel frames under fire situation, and proposes a new methodology based on plastic global analysis to estimate the resistance of such structures under fire situation accounting for their redistribution capacity, improving the accuracy of the predicted fire time resistances significantly for the two materials.

Mechanical properties and JC constitutive modification of tungsten alloys under high strain rates and high/low temperatures

The original Johnson-Cook model's poor prediction of W90 alloy stress at high strain rate and high and low temperatures restricts research and utilization of this alloy. This study used a Split Hopkinson Pressure Bar (SHPB) device to conduct dynamic compression tests on W90 alloy over a temperature range of [-90℃,700℃] and analyze its mechanical behavior. We examined the material's different plastic phase characteristics at high and low temperatures and conducted microstructure research on impact test specimens. Then, we analyzed the stress-strain data from SHPB experiments and quasi-static compression tests on the classical Johnson-Cook model. The original Johnson-Cook model was calibrated using the stress-strain data from SHPB and quasi-static compression tests, and the modified Johnson-Cook model was established and verified. The results show that: low temperature significantly strengthens the material's stress, while increasing temperature thermal softening reduces stress; increasing strain rate increases the strain generated by the workpiece, causing faster strain hardening and thermal softening effects, resulting in higher and more stable stress; low temperature makes thicker grain boundaries, increasing plastic stress, and increasing strain rate also increases plastic stress, as well as making the material's grain boundaries thicker. The increase of strain rate makes the grain more dense, which will also show up in the increase of stress on the macroscopic level; the modified Johnson-Cook model in this paper has high agreement with experimental data, with a mean value of MAPE of only 1.85 %,which is 90.20 % lower than the traditional model, and the average value of the RMSE is 85.56 % lower than the traditional model. The modified model significantly outperforms the traditional model in predicting stress and better describes stress changes in W90 at different temperatures.

Influence of strength difference between soft and hard zones on hetero-deformation induced strengthening effect: Taking heterostructured β Ti alloy as an example

The large strength difference between soft and hard zones in heterostructured materials is a double-edged sword: on the one hand, the effective back (τb) and forward stress (τf) are generated to produce hetero-deformation induced (HDI) strengthening and strain hardening effect. On the other hand, the micro-cracks tend to initiate and propagate along the interface to cause premature failure. Here we prepared three different heterostructured Ti-4.8Al-5.6Mo–3V-1.5Cr-1.6Fe alloys to reveal the influence of magnitude of strength difference between soft primary α phase (αp) and hard β matrix on its tensile strength and ductility. It demonstrates that only when the sum of applied stress (τa) and τf is greater than the yield strength of hard β matrix (σyhard), i.e., τa+τf>σyhard, the alloy can obtain both high strength and ductility. Contrary, when τa+τf<σyhard, the alloy exhibits a highest strength but a lowest ductility. These findings are expected to help with designing heterostructured materials for superior mechanical properties.

Low cycle fatigue and cycle hardening behavior of heterogeneous Ni2Co1Fe1V0.5Mo0.2 medium entropy alloy

Low-cycle fatigue behavior of high-entropy alloy (HEAs) and medium-entropy alloys (MEAs) have rarely been reported in literature though it is critical for industrial applications. In our previous work, a non-equiatomic Ni2Co1Fe1V0.5Mo0.2 MEA was designed by adding V and Mo elements with bigger atomic size to heighten solution strengthening effect. Due to larger atomic size mismatch and more severe lattice distortion, the Ni2Co1Fe1V0.5Mo0.2 MEA exhibits stronger strain hardening effect than that in CoCrFeMnNi HEA. In present work, the low-cycle fatigue behavior of the non-equiatomic Ni2Co1Fe1V0.5Mo0.2 MEA with heterogeneous grain structures was further investigated. The heterogeneous Ni2Co1Fe1V0.5Mo0.2 MEA exhibits high fatigue resistance at 0.25 % strain amplitude (51285 N), attributed to the pronounced dislocation planar slip and formation of stacking faults. At 0.3 % and 0.5 % strain amplitudes, dislocation interactions (including tangles and microbands) induced by extensive dislocation cross-slip result in obvious cyclic hardening but reduced lifetime. The findings assess the effect of solid solution strengthening on the fatigue behavior of MEAs. The fatigue cracks form either along slip bands in large grains or grain boundaries of small grains.

Hierarchical H-bonding and metal coordination bonds enabled supramolecular dual networks for high-performance energy-dissipation

Natural organisms have superior material properties such as mechanical adaptability, impact protection, and self-healing to protect the body from complicated external environments, fascinating the development of functional supramolecular elastic materials with biomimetic protective features. Herein, a dual physically crosslinked supramolecular polyurethane (PU) network with strain-hardening effect is synthesized by incorporating hierarchical hydrogen bonds (H-bond) and metal coordination bonds into an elastomer matrix. A moderate content of quadruple H-bonds is critical for achieving a prominent toughness and a considerable strain-at-break owing to the strain hardening effect enabled by the hierarchical H-bonds. When the Zn-to-pyridine coordination bonds were introduced to the supramolecular PU, the strength, toughness, and energy dissipation properties were further enhanced attributing to the dual physical crosslinking networks. The dynamic dissociation and association of the sacrificial H-bonds and Zn-to-pyridine coordination bonds induced significant strain hardening effect and enabled tremendous energy absorption and self-healing properties. Besides, the supramolecular PU elastomers and their blends were foamed via scCO2 foaming to produce supramolecular foams containing dynamic bonds. The composite foam could effectively reduce the impact force from 6085 N to 373 N and achieve an outstanding energy absorption efficiency of 93.87% owing to the synergistic effect of porous structure and dual physically crosslinked networks. This work provides an innovative strategy for designing high-performance energy absorbing supramolecular elastomers and cushioning foams with reversible bonds.

Dynamic tensile behavior and rate-dependent constitutive model of 304 + Q235 bimetallic steel

This paper aims to elucidate the rate-dependent behavior of 304 + Q235 bimetallic steel under intermediate strain rates. Tensile tests were conducted on 18 sets of specimens to obtain the engineering stress-strain curves at various strain rates. The experimental results demonstrate that the strain rate significantly influences both the yield strength and ultimate strength of the 304 + Q235 bimetallic steel, albeit with different trends. The yield strength exhibits an upward trend with increasing strain rates, whereas the ultimate strength demonstrates a downward trend. Additionally, the strain-hardening effect diminishes proportionally with the increase in strain rate. The parameters of the Cowper-Symonds model associated with the dynamic yield strength increase factor (DIFy) were determined based on the experimental findings. A bilinear rate-dependent constitutive model was established to accurately predict the dynamic ultimate strength increase factor (DIFu) of 304 + Q235 bimetallic steel. The established bilinear model was utilized to enhance the Johnson-Cook model for accurate prediction of the true stress-strain behavior of 304 + Q235 bimetallic steel under intermediate strain rates. The calculated results obtained from the modified Johnson-Cook model exhibit good agreement with the experimental results.

An Experimental Study on the Thermomechanical Coupling Effects of Carbon-Fiber-Reinforced Polyetheretherketone under Dynamic Impact.

Carbon-fiber-reinforced polyetheretherketone (CF/PEEK) composites are widely utilized in aerospace, medical devices, and automotive industries, renowned for their superior mechanical properties and high-temperature resistance. Despite these advantages, the thermomechanical coupling behavior of CF/PEEK under dynamic loading conditions is not well understood. This study aims to explore the thermomechanical coupling effects of CF/PEEK at elevated strain rates, employing Hopkinson bar impact tests and scanning electron microscopy (SEM) for detailed characterization. Our findings indicate that an increase in temperature led to significant reductions in the yield strength, peak stress, and specific energy absorption of CF/PEEK, while fracture strain had no significant effect. For instance, at 200 °C, the yield strength, peak stress, and specific energy absorption decreased by 39%, 37%, and 38%, respectively, compared to their values at 20 °C. Furthermore, as the strain rate increased, the yield strength, peak stress, specific energy absorption, and fracture strain all exhibited strain-hardening effects. However, as the strain rate further increased, above 4000 s-1, the enhancing effect of the strain rate on the yield strength and peak stress gradually diminished. The interaction of the temperature and strain rate significantly affected the mechanical performance of CF/PEEK under high-speed impact conditions. While the strain rate generally enhanced these properties, the strain-hardening effect on the yield strength weakened as the temperature increased, and both the temperature and strain rate contributed to the increase in specific energy absorption. Microdamage mechanism analysis revealed that interface debonding and sliding between the fibers and the matrix were more pronounced under static compression than under dynamic compression, thereby diminishing the efficiency of stress transfer. Additionally, higher temperatures caused the PEEK matrix to soften and exhibit increased viscoelastic behavior, which in turn affected the material's toughness and the mechanisms of stress transfer. These insights hold substantial engineering significance, particularly for the optimization of CF/PEEK composite design and applications in extreme environments.

A method to represent the strain hardening effect in the hyper-elastic model within a fully Eulerian framework

We propose a method to treat the strain hardening effect in the hyperelastic model. Coupled with the level set interface capturing method and a real ghost fluid method, it is formulated in a fully Eulerian framework. The HLLD approximate Riemann solver is used to obtain the interface state. We use the elastic inverse deformation gradient tensor to track the material deformation state. Once the solid starts to yield, along the normal direction in stress space, an iterative algorithm is used to relax the elastic inverse deformation gradient tensor to target value where the equivalent stress meets the requirement of consistency condition in plasticity. This approach is intuitive and can avoid the use of the physical delay time, which is difficult to calibrate from experiments. We use the Wilkins flying plate impact, cylindrical shell collapse, Taylor impact and the conical-nosed projectile penetration test cases to validate the method. The results show good agreement with the theoretical analysis and experiments. This approach can also apply without further extension when thermal softening effect or damage models are considered.

Research on post-fire mechanical properties of thin-walled cold-formed steel and its influence on the Σ-shaped columns after fire exposure

This paper conducts a comprehensive investigation into the post-fire mechanical properties of thin-walled cold-formed steel (CFS) and evaluates the design method for the post-fire load-bearing capacity of CFS lipped channel section with web stiffener (Σ-shaped) columns. A total of 144 tensile tests were conducted to determine the mechanical properties of CFS after exposure to heating treatment. The study considered the effects of varied material strengths (Q235 and Q420), plate thicknesses (1.5 mm and 2.5 mm), extraction positions (flat plate, 90° corner, and 45° corner), as well as heating temperatures ranging from 20 °C to 800 °C. The research indicates that the heating temperature does not have a prominent influence on the elastic modulus of CFS, whereas its impact on yield strength is pronounced. After exposure to 800 °C, the yield strength of CFS can be reduced by 40 %, but the strain-hardening effect by cold-working still existed, which enhanced the yield strength by up to 20 %. This paper presents a predictive formula for the reduction factor of the mechanical properties. To assess the influence of post-fire mechanical properties on the load-bearing capacity of CFS columns, a finite element model of Σ-shaped columns was developed and calibrated. The simulation results indicate that the post-fire strain-hardening effect at corners would enhance the load-bearing capacity by less than 6 %. Finally, based on a parametric analysis, it was demonstrated that the Direct Strength Method (DSM) applied for distortional-local interaction buckling columns was still effective once the post-fire mechanical properties were incorporated when slenderness factor λdl > 1.5.

A Study on the Fracture Toughness Evaluation Considering Material Tensile Characteristic for Cryogenic Steel

Abstract ISO 12135, a representative standard for the evaluation of fracture toughness, was revised in 2021. In the previous standard published in 2016, only yield strength was reflected for material property in fracture toughness calculation. In the revised standard, however, yield to tensile strength ratio is additionally reflected in consideration of strain hardening effect of the material. The current fracture toughness calculation formula evaluates fracture toughness reasonably considering the tensile characteristic. However, in some cases of cryogenic steels, fracture toughness is evaluated very conservatively than the previous procedure in 2016. In the case of STS 304L, there is no ductile-brittle transition phenomenon and it has excellent ductility and strength in cryogenic temperature. However, due to the secondary hardening phenomenon, yield to tensile strength ratio is relatively low, and as a result, fracture toughness is evaluated very low. The target of this study is to resolve the undervaluation of fracture toughness of cryogenic steel in the revised ISO 12135. For this purpose, the elastic and the plastic parameters in crack tip opening displacement (CTOD) equation in ISO 12135 are examined. The crack tip profile is derived by a series of finite element analysis and crack tip opening displacement is calculated for the derivation of new parametric equations for cryogenic materials. The calculated crack tip opening displacement is validated by experimental results.

Evolution of microstructure and mechanical properties of Ti65 high-temperature titanium alloy after additive manufacturing and annealing

Ti65 was prepared by Laser Direct Energy Deposition (LDED) and subjected to Annealing Heat Treatment (AHT). The microstructure and mechanical properties of different specimens were evaluated. The results indicated that the prior β columnar crystals had a strong [0001] texture along the grain growth direction. The coarsening or spheroidization of α lath was attributed to the splitting of lamellar α, subsequent non-directional growth, element migration, and Ostwald ripening. The isotropy of the specimen annealed at 950 °C was caused by trimodal microstructure, discontinuous grain boundary α (αGB), precipitates dissolution, and low-angle grain boundary. A mathematical model was established to predict yield strength (YS) and microhardness based on the α lath thickness. The microhardness-strength correlation of LDED Ti65 followed an empirically derived model (Tabor's relationship). Improvements to the original models of the microhardness-strength relationship for Ti65, in conjunction with the strain-hardening effect and α orientation, made it possible to use these models to predict the strength of LDED Ti65 parts and improve the accuracy of the predicted values. Simultaneously, the model can provide data support for the industrial application of Ti65 or, where appropriate, provide a reference for other technical production (material applications).

Effect of the cyclic loading on the yield surface of a chemically stabilised soil

When a soil is subjected to cyclic loading, there are changes in the material's geomechanical behaviour that need to be characterised before safely designing any future projects. In terms of cyclic loading, it is important to characterise not only the failure of the soil but also its behaviour before failure, in particular the yield point and the elastic behaviour of the material. This study examines the effects of the number of loading cycles on the behaviour of a chemically stabilised soft soil with a particular focus on the yield surface. To this end, a series of triaxial tests were performed on specimens, previously or not subjected to a different number of loading cycles (1000–100 000). The results were analysed in terms of the evolution of accumulated permanent axial strain, the yield surface and stress–strain behaviour. It was observed that an increase in the number of loading cycles promoted: an increase in the permanent axial strain, an increase in the undrained resilient modulus, a shrinkage of the yield surface but its shape is maintained, and there is a small increase in the peak strength of the stabilised soil explained by the strain-hardening effect induced by the cyclic loading.

Ultrastrong and ductile W–Cu composites via Al- mediated interfacial diffusion layers and matrix-nanoclusters networks

W–Cu composites are integrated materials with both structural and functional properties. However, the weak interfacial bonding capability leads to limited strain hardening, which makes it difficult to take full advantage of the coordination of the biphasic materials. In present work, a multistage strain-hardening (MSH) effect is created, which enables the W–Cu composites to possess a persistent and effective strain-hardening capability. The prepared W-30(CuAl5) (wt.%) alloy has significant tensile ductility (∼21 %) and ultra-high yield strength (∼840 MPa). Remarkably, compared to the original W–30Cu without Al alloying, the strength and ductility are over two and three times, respectively, accompanied by the preservation of an electrical conductivity of about 80 %. This excellent synergistic effect stems from the Al-mediated interpenetrating interfacial diffusion layers and matrix-nanoclusters interconnection networks. As a result, a high-density of dislocation segments, self-locking structures, and a variety of twinning mechanisms such as nanotwins and 9R configurations are sequentially activated, allowing the composites to accommodate ductility deformation while simultaneously facilitating interactions that produce three unusual rises in strain-hardening rate. The present work offers a critical perspective on the realization of a synergistic ultrahigh tensile ductility and strength combination in metal matrix composites.

Effect of high strain rate on adiabatic shear susceptibility and microstructures in Al0.4CoCrFeNi high-entropy alloy

The effect of high strain rate on adiabatic shear susceptibility and microstructures in Al0.4CoCrFeNi high-entropy alloy (HEA) was examined using a split Hopkinson pressure bar (SHPB) and hat-shaped specimens. The results exhibit a clear strain-hardening effect at high strain rates within the experimental range in six specimen groups. The adiabatic shear band (ASB) with an approximately 1 μm wide was formed at 1.05 × 105 s−1 due to thermoplastic instability resulting from adiabatic temperature rise. The central region of the ASB consists of ultrafine and equiaxed recrystallized grains with a typical size of 100 nm. Comparison of metallographic observation and calculation shear voltage-time, the dynamic shear stress-time curves and the dissipation energy, it was found that the adiabatic shear susceptibility of Al0.4CoCrFeNi HEA increases with increased strain rate. The thermodynamic and kinetic calculations indicate that dynamic recrystallization can occur in the shear band based on the rotational dynamic recrystallization (RDR) mechanism.

Experimental and constitutive model investigation on the tensile mechanical properties of polyurea at wide strain-rate range

Polyurea is extensively utilized as a protective coating material for structures under impact and blast loadings, owing to its significant large tensile deformation capability and strain hardening effect. In this study, the tensile performance of polyurea was experimentally and theoretically investigated. Firstly, rational geometric shapes and dimensions were designed, and a series of quasi-static and dynamic uniaxial tensile tests were conducted to obtain the nonlinear stress-strain curves at different strain rates. The results indicated a notable strain-rate effect in polyurea, with an increase in elastic modulus and tensile stress as the strain rate increased. Moreover, as the strain rate escalates, the strain hardening effect becomes more pronounced, thereby enhancing the protective capabilities of polyurea. Subsequently, an existing hyperelastic model, namely the Mooney-Rivlin (MR) model, was modified to incorporate the strain rate effect, resulting in a non-linear visco-hyperelastic constitutive model. Furthermore, the proposed constitutive model and parameters were validated by simulating existing tensile and blast tests using the finite element (FE) program LS-DYNA. This work could provide a reference for the design of structural protection.