Large Plastic Deformation Research Articles

Facile Construction of Polypropylene Foam with Dense Oriented Cell Structure and Enhancing-ductility Mechanism

Common polypropylene (PP) foam exhibited intrinsic inferior ductility and mechanical strength, which restricted its application as lightweight structural parts. To improve the ductility and mechanical strength of PP foam, the highly oriented PP component with fibrillar structure (cold-drawn fiber, CDF) was blended with isotropic PP resin to prepare PP/CDF foam via a facile foam injection molding process. During foaming at 170°C, CDF was not melted completely. Then, the remaining fibrils acted as shish structure and induced the crystallization of PP chains on its surface to form oriented kebab crystals, and the viscoelasticity and melt strength of the system were significantly improved, which promoted the nucleation of the bubble and the elongation of the cells, constructing a dense oriented cell structure with a large number of slender cylindrical cell walls for the foam. Such cell wall structure was prone to large plastic deformation and continuous elongation under load, which reduced stress concentration and absorbed a significant amount of tensile energy. As a result, a ductile and strong PP/CDF foam was successfully constructed, which exhibited roughly 465% increase in strain at break and 15% increase in tensile strength, respectively compared with PP foam.

Study on Large Plastic Deformation Mechanism of AlCoCrFeNi2.1 Eutectic High-Entropy Alloys Prepared by Laser Additive Manufacturing

Study on Large Plastic Deformation Mechanism of AlCoCrFeNi2.1 Eutectic High-Entropy Alloys Prepared by Laser Additive Manufacturing

Micromechanical characteristics of titanium alloy (Ti-6Al-4V) made by laser powder bed fusion using an in-situ SEM micropillar compression technique

While titanium alloy (Ti-6Al-4V) made by laser powder bed fusion (L–PBF) exhibits complex deformation behaviors, its important micromechanical properties in relation to loading directions are not fully understood. This research aims to investigate the micromechanical behaviors of printed L–PBF Ti-6Al-4V alloys under vertical (i.e., the loading direction perpendicular to printed layers) and horizontal (i.e., the loading direction parallel to printed layers) compressions using in-situ scanning electron microscopy (SEM) micropillar techniques. Ti-6Al-4V alloys were L-PBF-printed using a 45° rotate scanning strategy with vertical and horizontal build directions. The microstructures of the two alloys were analyzed using the SEM with energy-dispersive X-ray spectroscopy (EDS). The titanium alloy micropillars were produced using focused ion beam (FIB) milling in the SEM. In-situ SEM micropillar compressions were conducted using a flat diamond indenter. Vertical alloy had smaller cross-patterned finer α′ martensite than horizontal one. While both vertical and horizontal micropillars showed elastic-plastic behaviors, the former had significantly higher yield, fracture, and compression strength values, as well as resilience and toughness, than the latter, leading to the formation of favorable shear bands. Both micropillars exhibited ductile fractures but had distinct failure mechanisms. The ductile fracture in the vertical micropillars was due to strain hardening, large plastic deformation, and shear band formation, while the ductile fracture in the horizontal ones was attributed to compression-induced bending and plastic buckling. The micromechanical characteristics of L–PBF Ti-6Al-4V materials provides an important insight into the small-scale deformation and failure mechanisms of the alloys influenced by loading directions.

In-Plane Cyclic Mechanical Properties of CF/PEEK/TPU Flexible Composite with Zero Poisson Ratio.

This paper presents the in-plane deformation and cyclic mechanical properties of CF/PEEK (Carbon Fiber-Reinforced Polyetheretherketone)-reinforced TPU (thermoplastic polyurethanes) flexible composites with a zero Poisson ratio. A novel CF/PEEK honeycomb reinforcement with a zero Poisson ratio was fabricated by using 3D-printing technology. Then, TPU was bonded in the two sides of the CF/PEEK honeycomb reinforcement. The in-plane deformation ability and cyclic mechanical properties were evaluated. The results show that the zero Poisson ratio flexible composite can achieve a large in-plane plastic deformation of more than 50% and can better maintain the zero Poisson ratio superstructure. By collecting and comparing the mechanical characteristic values of the CF/PEEK flexible composite under a cyclic load, the CF/PEEK flexible composite MH22-t0.6-CT has the best structural stability. The length of the structure was increased by about 12.53%. By studying the deformation mechanism and failure mechanisms of the flexible composites, the in-plane recyclability of the flexible composites was evaluated, which provides the basic research basis for large-scale in-plane deformation composites.

Multi-functional additively constructed honeycomb walls for housing and sheltering

Honeycomb designs have become increasingly popular in additive manufacturing due to their great mechanical properties. The honeycomb infill pattern has allowed the creation of lightweight objects without sacrificing the strength of solid objects. Honeycombs have been utilized in different applications, including architecture, aerospace, and automotive. However, there is a lack of honeycomb designs within the construction industry. With the growth of concrete additive construction, there is an opportunity to introduce honeycomb designs into construction practices. This paper proposes a methodology for manufacturing multi-functional walls through additive construction. The methodology includes several key steps, from material development and quality control testing to wall assembly and experimental investigation. Two multi-functional wall segments were additively constructed, reaching a height of 1180 mm, a width of 610 mm, and a thickness of 90 mm. These measurements led to the manufacturing of seven distinct cellular sections per wall, comprising three main, two intermediate, and two end cellular units. In addition, a columnar unit was additively constructed for corner connection, featuring two vertical octagonal cells with end brackets. A preliminary wall system made up of honeycomb wall segments was assembled using various additional materials such as sealant, clamping systems, and insulative materials. Furthermore, an additional wall segment with end connections was designed and manufactured to test its load-carrying capacity. The wall segment performed well compared to wooden stud walls and showed sufficient load-carrying capacity. Unlike traditional un-reinforced concrete structures, which are brittle and experience small plastic deformations before failing, the honeycomb wall structure experienced large plastic deformation before failure due to the use of insulation foam and silicon rubber. The preliminary testing showed that the honeycomb wall system could be an alternative to traditional housing construction, especially for shelters.

Research on the ultra-low temperature tensile deformation mechanism of Al-Mg-Si alloys in different heat treatment states

The susceptibility of Al-Mg-Si alloy to cracking during room temperature large plastic deformation poses a significant obstacle to its widespread application. Cryogenic temperature forming of aluminum alloys has emerged as a prominent research topic. However, the precise mechanisms underlying the enhancement of aluminum alloy plasticity in different states remain elusive. In order to elucidate this matter, a series of uniaxial tensile experiments were conducted on Al-Mg-Si alloy featuring diverse initial states, under varying temperature conditions. The results show that when the deformation temperature is reduced from 25℃ to −196℃, the tensile strength and elongation of the wrought material are increased by 48 MPa and 5.42 %, and the tensile strength and elongation of the annealed material are increased by 118 MPa and 5.65 %. In contrast, while the T4 state sample exhibited a significant improvement in tensile strength (103 MPa), no substantial enhancement in elongation was observed. This disparity can be primarily attributed to the absence of second-phase precipitation in the as-forged and annealed states. As the temperature decreased, the critical shear stress increased, resulting in increased resistance to deformation. Consequently, an increased degree of lattice rotation and activation of dislocations in various slip systems ensued, thereby improving the deformation uniformity. The formation of initial microvoids predominantly occurred close to grain boundaries. Therefore, compared with room temperature deformation, low temperature deformation caused by the accumulation of dislocations and hole sprouting concentrated at a single location was less likely. As a result, the dislocation distribution was more uniform and fracture was less likely to occur. Conversely, in the T4 state, the aging process resulted in the precipitation of a substantial amount of the soluble second phase (Mg5Si6). Consequently, microvoid nucleation transpired at the phase boundaries, leading to an elevated tensile strength. However, because of the increased dislocation hindrance when the deformation temperature was lowered, no significant enhancement in plasticity was observed.

Out-of-plane energy absorption of 3D printed basalt-fiber-reinforced hierarchical honeycomb composite

This work presents a new type of hierarchical triangular honeycomb created by iteratively replacing each vertex of conventional hexagonal cells with a smaller equilateral triangle. The combination of green and recyclable short basalt-fiber-reinforced composite with advanced additive manufacturing technology makes it possible to design and fabricate the 3D printed hierarchical triangular honeycomb composites with exceptional mechanical properties for energy absorption applications. Out-of-plane quasi-static compression tests were performed on the 3D printed hierarchical honeycomb composite to investigate the compressive response and deformation behaviour of hierarchical triangular honeycombs. Parametric studies were conducted using ABAQUS/Explicit finite element code to study the effects of structural hierarchy and triangular cell size on mechanical properties and energy absorption of 3D printed hierarchical triangular honeycombs. The result revealed that the 3D printed hierarchical triangular honeycomb composite experienced a large and stable plastic deformation to densification without fracture failure resulting in excellent energy absorption. The second level triangular honeycomb composite exhibited the most promising mechanical properties. After optimization of the triangular cell size, the mean crushing force and specific energy absorption of the second level triangular honeycomb composite were about 1.7 times and 2.0 times those of the conventional hexagonal honeycomb composite. Compared to other typical hierarchical honeycombs, the proposed hierarchical triangular honeycomb composite exhibited higher plateau stress and larger densification strain, thus providing some insights in designing lightweight, recyclable and sustainable 3D printed honeycomb composites with superior mechanical properties.

Implementation of the Zienkiewicz–Pande Model into a Four‐Dimensional Lattice Spring Model for Plasticity and Fracture

ABSTRACTPlasticity and fracture problems have always been hot topics in numerical methods. In this work, a universal implementation procedure for the elasto‐plastic constitutive model is developed in the four‐dimensional lattice spring model (4D‐LSM), in which the Jaumann stress rate is incorporated to exclude the influence of the rigid rotation in the particle stress, expanding the ability of 4D‐LSM to deal with large elastic deformation problems by its own to large plastic deformation problems. As an example, the Zienkiewicz–Pande (ZP) constitutive model is implemented. Several numerical examples are carried out to check the performance of the implemented model. Through a comparison with analytical solutions, available experimental data, and other numerical results, the stability of the developed plastic framework and the correctness of the stress calculation scheme are verified. Meanwhile, numerical results show that the developed code is capable of solving elasto‐plastic large deformation problems. With the advantage of 4D‐LSM in handling fracture problems, the ability of the embedded model to solve plastic fracture problems is verified with a simple maximum deformation failure criterion.

Determination of the plastic J integral of ductile material using the XFEM with only Heaviside function and variable-node elements

In this paper, the extended finite element method (XFEM) with only Heaviside function is proposed for the elastic–plastic fracture mechanics (EPFM) modeling. The proposed method removes tip enrichment functions depending on the polar coordinates at the crack front, and a step function only determined by the level set function is utilized to track the crack front. To alleviate the volumetric locking phenomena caused by the plastic incompressibility, the B-bar method is incorporated into the three dimensional (3D) XFEM program. Therefore, the fully integration scheme can be chosen to ensure the accuracy when addressing large plastic deformation in EPFM analysis. Additionally, the material tangent stiffness matrix of Ramberg-Osgood constitutive is given, and the local refinement technique using variable-node elements is adopted to reduce the number of elements and nodes for efficient analysis. A Newton-Raphson iterative algorithm is developed to solve the nonlinear algebraic equations caused by material nonlinearity. Several numerical examples including the determination of crack opening displacement, and the fully plastic J integral in the ductile materials are presented to test the performance of the proposed method. Comparisons with the results from the existing methodologies show that the new enrichment scheme can save computational cost and obtain sufficient accuracy even in the case of 3D curved crack.

Making large-size fail-safe steel by deformation-assisted tempering process

Synergistically improving the strength and toughness of metallic materials is a central focus in the field of physical metallurgy. Yet, there is a noticeable lack of research in strengthening and toughening large-size metal components, whereas those components are extensively used in the modern industry. In this work, a deformation-assisted tempering (DAT) process was proposed to create a novel microstructure in 1.4 tons low-alloyed plain steel. After DAT treatment, the steel contains low dislocation density but high density of low-angle subgrain boundaries and dispersed spherical nano carbides. Such microstructure enables a much better combination of tensile strength and fracture toughness compared to the small-size quench and temper steels. The significant improvement in low-temperature impact toughness is due to the occurrence of delamination and subsequent large plastic deformation at the notch tip. The DAT process can provides a new strategy for the development of large-size fail-safe steel with excellent strength and fracture resistance.

Solid face sheets enable lattice metamaterials to withstand high-amplitude impulsive loading without yielding

Owing to their ability to provide tunable mechanical responses, lattice materials are frequently studied to elucidate their response to static and dynamic loads. However, these roles are typically in opposition: static loads must be supported sufficiently far away from the onset of buckling or yielding, whereas dynamic loads are typically ameliorated by crushing of the lattice, which provides excellent energy-absorption due to the large plastic deformation accompanying densification. In contrast, this work considers the octet truss as an exemplar topology, in a structural role where it must simultaneously support static loads while enduring high-amplitude impulsive loads. This study focuses on the ability to withstand impulsive loads without yielding, an essential prerequisite to enduring dual loading. Computational studies using the ALE3D hydrocode were performed to examine the response of the octet truss under a short temporal width impulse shape associated with laser-driven shocks. A key finding was that covering the lattice with a solid face sheet and treating this face sheet thickness as a design variable allows the Taylor-like pulse to be attenuated prior to entering the weaker lattice, at the cost of added mass up front. Experimental validation was accomplished by laser-driven shock testing, using octet trusses printed out of Ti-5Al-5V-5Mo-3Cr. The results show that for a given quantity of mass, the attenuation is maximized when as much mass as possible is moved into the face sheet, leaving a more slender lattice structure. The effect of placing mass in the face sheet rather than lattice beams dominates the effect of relative density, to the point where a low-mass structure with most of the mass concentrated in the face sheet can outperform a high-mass structure with most of the mass in the lattice. By further understanding the propagation of short pulse width waves within under-dense structures, this study expand the domain of applicability of such structures, including lattice materials, to challenging dual-loading regimes spanning decades of strain rates.

Material plasticity – Development of stiffness tetrads in fiber‐reinforced materials with large plastic deformations

AbstractThe main objective of this work is to follow the evolution of the stiffness tetrad during large plastic strains. For this purpose, the framework of a general theory of finite plasticity is developed. Some special cases are investigated and the case of a material plasticity theory is considered in more detail. Its main feature is that the elasticity law changes during plastic deformations, for which we develop an approach. We use three types of fiber‐reinforced composites as example materials. Finite element simulations of representative volume elements for uni‐, bi‐ and tri‐directionally reinforced materials with periodic boundary conditions are used for numerical experiments and verification of the model's predictions. From these, we extract the stiffness tetrads before and after large deformations of the material. We quantify the change in stiffness tetrads due to fiber reorientation. Finally, we propose an analytical evolution with three parameters that reproduces reasonably well the evolution of the stiffness tetrads.

Towards a Direct Consideration of Microstructure Deformation during Dynamic Recrystallisation Simulations with the Use of Coupled Random Cellular Automata-Finite Element Model.

Dynamic recrystallisation (DRX) is one of the fundamental phenomena in materials science, significantly impacting the microstructure and mechanical properties of components subjected to large plastic deformations. Experimental research on that topic carried out for a wide range of new metallic materials is often supported by computational materials science. A direct consideration and detailed understanding of this phenomenon are possible with a class of full-field numerical models based on the cellular automata (CA) method. However, the classical CA approach is based on a regular, fixed computational space and has limitations in capturing large deformations of the computational domain. Therefore, the main goal of the work is to develop and implement an alternative solution to overcome this limitation. The proposed solution is based on coupling the finite element (FE) method with the random cellular automata (RCA) approach. Such a model can directly consider the influence of geometrical changes in microstructure during large plastic deformation on recrystallisation progress. Details of the developed RCA DRX model assumptions and coupling issues with FE mesh are discussed. Particular attention is also paid to increasing model efficiency and robustness studies.

Effect of overlapping deposition strategy on microstructure and mechanical properties of Al-clad steel by AFSD

Cladding of the aluminum (Al) layer on steel was successfully implemented via additive friction stir deposition (AFSD). We revealed the relationship between the overlapping deposition strategy of AFSD and the resultant microstructure and mechanical properties of Al-clad steel for the first time. Overlapping deposition strategies efficiently improved the adhesion of the Al layer on steel in the boundary region owing to the sufficient material flow and large plastic deformation. This is in contrast to the sample without overlapping where the Al/steel interface in the boundary region is characterized by holes and weak bonding. In particular, the maximum shear strength (109.0 MPa) was obtained for the sample with an overlap of 8 mm, even higher than that of the single-pass sample. This study provided a novel approach to the fabrication of large-scaled clad layers on hard substrates, and this strategy is expected to greatly contribute to the adoption of AFSD in the fields of cladding, joining, and coating.

Research Progress on the Microstructure Evolution Mechanisms of Al-Mg Alloys by Severe Plastic Deformation.

Al-Mg alloys are widely used as important engineering structural materials in aerospace engineering, transportation systems, and structural constructions due to their low density, high specific strength, corrosion resistance, welding capability, fatigue strength, and cost-effectiveness. However, the conventional Al-Mg alloys can no longer fully satisfy the demands of practical production due to difficulties caused by many defects. The high strength of Al-Mg alloys as non-heat treatment precipitation-strengthened alloys is achieved primarily by solid solution strengthening along with work hardening rather than precipitation strengthening. Therefore, severe plastic deformation (SPD) techniques can be often used to produce ultrafine-grained structures to fabricate ultra-high strength aluminum alloys. However, this approach often achieves the strengthening of material at the cost of reduced ductility. This paper comprehensively summarizes the various approaches of ultrafine/nanocrystalline materials for enhancing their plasticity, elaborates on the creation of a bimodal microstructure within the alloy, and discusses the formation of a nanotwin microstructure within the alloy and the incorporation of dispersed nanoparticles. The mechanisms underlying both the strengthening and toughening during large plastic deformation in aluminum alloys are summarized, and the future research direction of high-performance ultrafine crystalline and nanocrystalline Al-Mg aluminum alloys is prospected.

Multiphase-field analysis of the intermetallic compounds formation & evolution in friction stir welding of dissimilar Al/Mg alloys

It is essential to understand the formation and evolution mechanism of intermetallic compounds (IMCs) in friction stir welding (FSW) of dissimilar Al/Mg alloys to mitigate the deleterious effect of hard and brittle IMCs on the performance of dissimilar joints. To this end, a multiphase-field model with input variables of both temperature and strain rate is developed to study the whole IMCs formation and growth process at the Al/Mg bonding interface in weld nugget zone. The effects of diffusion, elastic deformation, and large plastic deformation on the generation and growth of IMCs are considered. The numerical simulation results indicate that due to the influence of high dislocation density, the higher diffusion coefficient of the Mg matrix leads to the nucleation of Al12Mg17 first. When IMCs grow into layers, the higher diffusion coefficient of Al3Mg2 leads to a faster growth rate of Al3Mg2 than that of Al12Mg17. The elastic energy caused by lattice mismatch between IMCs and matrix plays an inhibitory role in the growth of IMCs. Large plastic deformation in FSW causes an increase in both the stored energy which promotes the IMCs growth and the dislocation density which intensifies the diffusion process, causing IMCs to form at the interface in a short time. With the model, the IMCs evolution from generation to growth is quantitatively analyzed. The predicted thickness of IMCs matches well with the experimental measurements.

Study on the Aging Precipitation Behavior and Kinetics of Al-10.0Zn-3.0Mg-2.8Cu Alloy by Pre-Deformation Treatment.

In this paper, the effect of thermomechanical treatment process on the hardening behavior, grain microstructure, precipitated phase, and tensile mechanical properties of the new high-strength and high-ductility Al-10.0Zn-3.0Mg-2.8Cu alloy was studied, and the optimal thermomechanical treatment process was established. The strengthening and toughening mechanisms were revealed, which provided technical and theoretical guidance for the engineering application of this kind of high strength-ductility aluminum alloy. Al-10.0Zn-3.0Mg-2.8Cu alloy cylindrical parts with external longitudinal reinforcement were prepared by a composite extrusion deformation process (reciprocal upsetting + counter-extrusion) with a true strain up to 2.56, and the organizational evolution of the alloys during the extrusion deformation process and the influence of pre-stretching treatments on the subsequent aging precipitation behaviors and mechanical properties were investigated. The results show that firstly, the large plastic deformation promotes the fragmentation of coarse insoluble phases and the occurrence of dynamic recrystallization, which results in the elongation of the grains along the extrusion direction, and the volume fraction of recrystallization reaches 42.4%. Secondly, the kinetic study showed that the decrease in the activation energy of precipitation increased the nucleation sites, which further promoted the diffuse distribution of the second phase in the alloy and a higher number of nucleation sites, while limiting the coarsening of the precipitated phase. When the amount of pre-deformation was increased from 0% to 2%, the size of the matrix precipitated phase decreased from 5.11 μm to 4.1 μm, and when the amount of pre-deformation was increased from 2% to 7%, the coarsening of the matrix precipitated phase took place, and the size of the phase increased from 4.1 μm to 7.24 μm. The finalized heat treatment process for the deformation of the aluminum alloy tailframe was as follows: solution (475 °C/3 h) + 2% pre-stretching + aging (120 °C/24 h), at which the comprehensive performance of the alloy was optimized, with a tensile strength of 634.2 MPa, a yield strength of 571.0 MPa, and an elongation of 15.2%. The alloy was strengthened by both precipitation strengthening and dislocation strengthening. After 2% pre-stretching, the fracture surface starts to be dominated by dense tough nest structure, and most of them are small tough nests, and small and dense tough nests are the main reason for the increase in alloy toughness after 2% pre-stretching deformation.

Material Parameter Identification for a Stress-State-Dependent Ductile Damage and Failure Model Applied to Clinch Joining

Similar to bulk metal forming, clinch joining is characterised by large plastic deformations and a variety of different 3D stress states, including severe compression. However, inherent to plastic forming is the nucleation and growth of defects, whose detrimental effects on the material behaviour can be described by continuum damage models and eventually lead to material failure. As the damage evolution strongly depends on the stress state, a stress-state-dependent model is utilised to correctly track the accumulation. To formulate and parameterise this model, besides classical experiments, so-called modified punch tests are also integrated herein to enhance the calibration of the failure model by capturing a larger range of stress states and metal-forming-specific loading conditions. Moreover, when highly ductile materials are considered, such as the dual-phase steel HCT590X and the aluminium alloy EN AW-6014 T4 investigated here, strong necking and localisation might occur prior to fracture. This can alter the stress state and affect the actual strain at failure. This influence is captured by coupling plasticity and damage to incorporate the damage-induced softening effect. Its relative importance is shown by conducting inverse parameter identifications to determine damage and failure parameters for both mentioned ductile metals based on up to 12 different experiments.

Plasticity in single-crystalline Mg3Bi2 thermoelectric material.

Most of the state-of-the-art thermoelectric materials are inorganic semiconductors. Owing to the directional covalent bonding, they usually show limited plasticity at room temperature1,2, for example, with a tensile strain of less than five per cent. Here we discover that single-crystalline Mg3Bi2 shows a room-temperature tensile strain of up to 100 per cent when the tension is applied along the (0001) plane (that is, the ab plane). Such a value is at least one order of magnitude higher than that of traditional thermoelectric materials and outperforms many metals that crystallize in a similar structure. Experimentally, slip bands and dislocations are identified in the deformed Mg3Bi2, indicating the gliding of dislocations as the microscopic mechanism of plastic deformation. Analysis of chemical bonding reveals multiple planes with low slipping barrier energy, suggesting the existence of several slip systems in Mg3Bi2. In addition, continuous dynamic bonding during the slipping process prevents the cleavage of the atomic plane, thus sustaining a large plastic deformation. Importantly, the tellurium-doped single-crystalline Mg3Bi2 shows a power factor of about 55 microwatts per centimetre per kelvin squared and a figure of merit of about 0.65 at room temperature along the ab plane, which outperforms the existing ductile thermoelectric materials3,4.

Theoretical nonlinear force-displacement constitutive model of triangular-plate steel damper

Utilizing the inelastic deformation of a steel damper to dissipate seismic energy and control structural damage is a prevalent design strategy in a passive control field. Such a design strategy requires an explicit force-displacement constitutive model of the steel damper in both the elastic and plastic deformation phases. Currently, the nonlinear force-displacement relationship of the steel damper is mainly determined by quasi-static tests or numerical simulations which are generally time-consuming, and there is a lack of a theoretical and straightforward approach to determine the nonlinear force-displacement constitutive model of the steel damper. This study thus theoretically derives the nonlinear force-displacement constitutive model for a commonly used triangular-plate steel damper. The theoretical formula is derived based on the equal curvature assumption commonly applied to the triangular plate and is further modified based on the curvature shape function proposed in this study for the first time. After that, the force-displacement curves obtained from the theoretical formula are compared with those obtained from a large number of numerical simulations and several sets of quasi-static tests. The result shows that the theoretical formula derived based on the curvature shape function can better predict the nonlinear force-displacement curve of the triangular-plate steel damper, which significantly outperforms the theoretical formula derived based on the equal curvature assumption especially as the triangular-plate steel damper has a large plastic deformation. Furthermore, the influence factors of the strain-hardening phenomenon existing in the force-displacement curve of the triangular-plate steel damper are analyzed based on the modified theoretical formula. The result implies that the thickness-to-height ratio of the plate is the most significant factor for the strain-hardening behavior of the triangular-plate steel damper.