Elastic-plastic Large Deformation Research Articles

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. The method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

Elastic effects on the dynamic plastic deflection of pulse-loaded beams

Beams under intense dynamic pulse loading may experience large elastic-plastic deformation. Despite numerous studies have been conducted based on the rigid-perfectly plastic idealization of material, it is of great interest in both theoretical modeling and practical application to characterize and evaluate the effect of elastic deformation on the dynamic behavior of structures. This paper is aimed to examine the range of applicability of rigid-plastic theoretical solutions on large deflection of beams in response to dynamic pulse loading. The energy ratio R and the characteristic time ratio are first precisely defined by referring to the characteristics of a “plastic string”, which represents the ultimate status of beams under very large deformation. Based on the recently published complete solutions on the dynamic response of fully-clamped and simply-supported rigid-plastic beams subjected to uniformly distributed rectangular pressure pulse, the discrepancies in final deflection and in saturated impulse of the rigid-plastic theoretical predictions from the elastic-plastic simulation results are evaluated and analyzed. It is revealed that if the energy ratio R>5 (with no limitation to the pulse duration), the rigid-plastic solutions can provide reliable predictions on final deflection and saturated impulse for the usage in engineering design. Then, the effects of the key dimensionless parameters related to the energy ratio R (e.g., the structural and material parameters as well as the loading one) on the discrepancies in final deflection and in saturated impulse are thoroughly examined. Finally, a unified dimensionless stiffness is identified to characterize the combined effect of structural and material parameters. For the cases of ζ≤1.581, which represent most of the practically used beams, 1/(2R) and 1/(3R) could provide upper bounds to the absolute value of the discrepancy in final deflection for fully-clamped and simply-supported beams, respectively.

A local search scheme in the natural element method for the analysis of elastic-plastic problems

Natural element method (NEM) is a meshless method based on the Voronoi diagram and Delaunay triangulation. It has the advantages of the meshless method, and simplifies the imposition of essential boundary conditions. NEM has great potential to solve the problems with large deformation. However, the high computational cost for searching natural neighbors is one of the main problems in NEM. In this paper a local algorithm based on K-Nearest Neighbor is presented for searching natural neighbors. Compared with the global sweep algorithm and other local search algorithms, the proposed algorithm introduces K to reduce the search scope. The value of K can be adjusted adaptively with the distribution characteristics of local neighbors of the calculation point and so the search can reach the global optimal value. The search scope changes with the flow of nodes, avoiding the problem that the natural neighbors exceed the search scope and reducing the calculation error. The proposed approach realizes the meshless characteristic in the natural neighbor searching process. The approach was used to solve the elastic deformation of a cantilever beam and a porous structure and the large plastic deformation in metal forming process. The results show that the proposed approach has great significance to solve problems in the elastic-plastic large deformation of metals and it is efficient.

Inverse Design of Energy-Absorbing Metamaterials by Topology Optimization.

Compared with the forward design method through the control of geometric parameters and material types, the inverse design method based on the target stress-strain curve is helpful for the discovery of new structures. This study proposes an optimization strategy for mechanical metamaterials based on a genetic algorithm and establishes a topology optimization method for energy-absorbing structures with the desired stress-strain curves. A series of structural mutation algorithms and design-domain-independent mesh generation method are developed to improve the efficiency of finite element analysis and optimization iteration. The algorithm realizes the design of ideal energy-absorbing structures, which are verified by additive manufacturing and experimental characterization. The error between the stress-strain curve of the designed structure and the target curve is less than 5%, and the densification strain reaches 0.6. Furthermore, special attention is paid to passive pedestrian protection and occupant protection, and a reasonable solution is given through the design of a multiplatform energy-absorbing structure. The proposed topology optimization framework provides a new solution path for the elastic-plastic large deformation problem that is unable to be resolved by using classical gradient algorithms or genetic algorithms, and simplifies the design process of energy-absorbing mechanical metamaterials.

Theoretical prediction of cross-sectional deformation of circular thin-walled tube in large elastic–plastic deformation stage under lateral compression

The present paper focusing on the most important energy absorbing system of the circular thin-walled tubes or shells under lateral compression between two rigid plates, which is also a basic mechanical issue, studies the cross-sectional deformation in terms of the compressive force applying to the tube in the large elastic–plastic deformation stage during the lateral compressive process by both theoretical as well as finite element analysis (FEA) methods. Firstly a FEA simulation for the thin-walled tube’s lateral compressive process between two parallel plates is carried out to analyze the mechanical response and deformation characteristics, and then it is validated by tube’s lateral compressive experiment using digital image processing technology. Following the simulation results, some assumptions are proposed for theoretical derivation. Secondly focusing on the large elastic–plastic deformation stage (Stage II, in this paper), the compressive deformation of thin-walled tubes is divided into elastic and plastic regions according to the von Mises yield criterion. In elastic region the linear strain–displacement relations of shell theory and Hooke’s stress–strain relations are employed, and in plastic region the nonlinear large strain–displacement relations of doubly-curved shell theory and the power hardening rule are employed. Then considering both geometric and material nonlinearities, the equilibrium equation, which is a complicate integral equation with the variable upper limit, is derived using the principle of virtual work. It is solved by expanding the integrand as a set of polynomials power series. Then the predicted cross-sectional deformation in terms of the compressive force can be obtained by the iterative method. Finally some lateral compressive simulations involving various tubes with different geometric parameters are carried out, and the theoretical model is validated by comparison of the cross-sectional profiles predicted by theoretical model with those obtained by the simulations as well as other methods. At the same time, the applicable conditions of this model are discussed. This paper will play a positive role in studying the cross-sectional deformation for various shells under lateral compression in different application areas.

3D J-integral evaluation for solids undergoing large elastic–plastic deformations with residual stresses and spatially varying mechanical properties of a material

In this paper, a 3D J-integral based on the domain integral approach is presented for large deformation elastic–plastic fracture mechanics problems associated with residual stresses and spatially varying mechanical properties of a material. The proposed 3D J-integral has physical significance as the energy dissipation into the process zone. The derivations of the proposed J-integral are presented in detail. Through numerical examples, it is shown that the proposed J-integral is unconditionally path independent. The present formulation is a rigorous extension of the 2D-Tε∗ integral of Okada and Atluri to 3D.

Residual stresses and strains analysis in press-braking bending parts considering multi-step forming effect

Press-braking bending is a multi-step bending process and widely applied in the aerospace industry. Residual stresses and strains generated during the forming process play an important role in determining its forming parameters and bending path. This work aims to analyze the residual stresses and strains in press-braking bending parts using both the theoretical method and numerical method. First, the analytical model of residual stress and strain is established based on the elastic–plastic bending theory. Second, a fully finite element model of press-braking bending has been developed, and a procedure to simulate the multi-step bending process is presented by using the elastic–plastic large deformation finite element method. The simulation results are then compared with three-point bending experiments in terms of forming force and final shapes of the bent specimens, and excellent agreement is achieved. Finally, the results calculated from the analytical model are compared with the numerical results. The distributions of residual stresses and strains on the finished plate along the length and thickness direction, and particularly the multi-step forming effect on residual stresses and strains, are discussed. It is found that the residual stresses and strains decrease at the initial loading position along the thickness direction during the forming process of subsequent loading positions. With the same punch displacement, the residual stresses and strains at the initial loading position are less than those at the subsequent bending position.

Large deformations of a cylindrical tube with prestressed coatings

General theoretical relations for calculating the redistribution of the preliminary irreversible strain field during unloading or elastic loading of a medium are obtained for the nonlinear multiplicative gradient model of large elastic-plastic deformations. It is shown that the dynamics of elastic shock waves does not depend directly on the previously accumulated plastic strains. A formula for the plastic-strain rotation tensor is obtained. It is shown that rigid rotation of plastic strains under elastic shock waves can be jump-like. All results are obtained for the general case of model relations of isotropic media and are valid for both compressible and incompressible materials.

The Propagation of Elastic Disturbances in a Medium with Large Irreversible Preliminary Strains

General theoretical relations for calculating the redistribution of the preliminary irreversible strain field during unloading or elastic loading of a medium are obtained for the nonlinear multiplicative gradient model of large elastic–plastic deformations. It is shown that the dynamics of elastic shock waves does not depend directly on the previously accumulated plastic strains. A formula for the plastic-strain rotation tensor is obtained. It is shown that rigid rotation of plastic strains under elastic shock waves can be jump-like. All results are obtained for the general case of model relations of isotropic media and are valid for both compressible and incompressible materials.

Non-symmetric bifurcation and collapse of elastic-plastic thick-walled cylinders under combined radial and axial loading

Thick-walled cylinders, which are loaded by accidentally excessive internal or external pressure, axial force or both, may fail due to non-symmetric bifurcation modes with multiple axial and peripheral waves. These failure modes are most relevant to submarines, onshore- and offshore pipelines, vacuum containers, subsea structures, and pressure vessels. Continuum theory is adopted to analyze the bifurcation behavior of such cylinders, considering large elastic-plastic deformation with non-linear hardening. The presented general comprehensive solution is capable of calculating the loads and deformation at the onset of bifurcation for modes of any order in both axial and peripheral directions. As a case study, several bifurcation limit curves of different orders have been calculated using the proposed theoretical solution for a closed thick-walled long cylinder loaded radially and axially. The results are validated numerically by FEA simulations using commercial software. Limit curves of column buckling (first order) and section-collapse (second or higher order) modes of bifurcation are calculated using the proposed solution. The results demonstrate that adding tensile or compressive axial force to external pressure loading delays the occurrence of the section-collapse bifurcation mode.On the other hand, adding external or internal pressure to an axial compression force, the axial strain at column buckling is also increased. The results also explain and quantify the transition between section-collapse and column-buckling bifurcation modes. While the presented results focus on different modes of non-symmetric buckling, the theory is also capable of calculating the axisymmetric and non-symmetric bulging as well as axial necking bifurcation modes. The presented solution offers deeper insight and substantial help to the designers of thick-walled cylindrical components of structures, particularly those subject to excessive external pressure, possibly combined with an axial force.

Insight into elastic–plastic bifurcation of pressurized cylinders: Transition between bulging and necking; the line of catastrophic failure

Bifurcation behavior of cylindrical pressure vessels simultaneously loaded by internal pressure and axial tension is investigated theoretically and numerically with emphasis on the transition between diffuse bulging and necking modes of bifurcation. It is illustrated that in very long cylinders, bifurcation occurs always instantly once instability is reached, resulting in catastrophic failure under all loading conditions. For short cylinders, both axisymmetric necking and bulging occur after the peak load, as steady deformation continues under falling loads before the occurrence of bifurcation. The delay is more obvious in shorter cylinders as axisymmetric bifurcation is delayed under some loading conditions so much that it does not occur, even after extremely large steady deformation under decreasing loads. A transition line, defined for any specified cylinder diameter-ratio, separates bulging and necking modes of bifurcation for all associated slenderness ratios. The delay of bifurcation after instability decreases significantly when a cylinder is loaded along the transition line, diminishes for thin walled cylinders, as localized necking occurs almost instantly, once the instability condition has been reached, leading to catastrophic failure. The style of bifurcation limit curves of thick-walled cylinders is generally similar to that of thin-walled cylinders. However, bifurcation of short thick cylinders is delayed noticeably, even when loaded along the transition line. Transition lines are defined and presented for cylinders with different diameter ratios. Axisymmetric bulging and necking bifurcation limits are displayed in correlation with the corresponding transition lines. The theoretical analysis is based on the continuum theory, takes into account large elastic–plastic deformation and non-linear material hardening. The theoretical solution is validated by comparing the theoretical results with FEA simulation results using independent commercial software. The findings provide a clear mapping of the loading conditions, which should be avoided in order to delay or prevent catastrophic failure when pressurized cylinders are accidentally overloaded.

Bifurcation of elastic–plastic thick-walled cylindrical structures

This article presents theoretical analysis of the bifurcation behavior of metallic thick-walled cylindrical structures, extremely loaded by combined pressure and axial force. The analysis, which is based on the continuum theory, takes into account large elastic–plastic deformations and non-linear isotropic hardening. Bifurcation analysis investigates the uniqueness of the velocity field in the fundamental state, which adopts a constitutive law is based on the von Mises yield criterion. The solution successfully predicts load and deformation limits associated with the onset of bulging and buckling bifurcation of thick-walled cylindrical structures. The theoretical solution is validated by comparing the theoretically obtained results with those obtained independently using nonlinear finite element simulations utilizing the commercial FEA software Abaqus. As an example, the numerical solution is presented for a thick, relatively long cylinder. The results show that, for axially compressed long cylinders, axial deformations at column buckling increase with additional internal or external pressure. The results also explain and quantify the transition from axisymmetric bulging to column buckling bifurcation modes. It also explains the occurrence of non-symmetric (localized) bulging, which follows the axisymmetric bulging. The findings provide valuable information in the safety design of extremely loaded hollow cylindrical columns, thick-walled pressure vessels, piping and other cylindrical structures.

One-Dimensional Interaction of a Cylindrical Unloading Wave with a Moving Elastic–Plastic Boundary

The one-dimensional dynamic problem of the theory of large elastic–plastic deformations is considered for the interaction of an unloading wave with an elastic–plastic boundary. It is shown that before the occurrence of the unloading wave, the increasing pressure gradient leads to quasistatic deformation of the elasti©viscoplastic material filling the round tube, which is retained in the tube due to friction on its wall, resulting in the formation of near-wall viscoplastic flow and an elastic core. The unloading wave is initiated at the moment of the onset of slippage of the material along the inner wall of the tube. Calculations were conducted using the ray method of constructing approximate solutions behind strong discontinuity surfaces, and ray expansions of the solutions behind the cylindrical surfaces of discontinuities were obtained.

Simple and efficient analyses of micro-architected cellular elastic-plastic materials with tubular members

In a novel way, nature evolves cellular structures to obtain mechanically efficient materials. Natural cellular materials combine low weight with superior mechanical properties to provide optimum strength and stiffness at low density such as trabecular bone, hornbill bird beaks, and bird wing bones. Inspired by these naturally architected cellular materials, humankind has also developed lightweight cellular materials for a broad range of applications consisting of structural components, energy absorption, heat exchange, and biomaterials. In this paper we present a highly efficient computational method to predict the bulk elastic-plastic homogenized mechanical properties of low-mass metallic systems with architected cellular microstructures. The proposed methodology provides a computational framework for the analysis, design, and topology optimization of such cellular materials. With a view for Direct Numerical Simulation of a cellular solid or structure with millions of cellular members, and considering the plausible deformations in each member, each such member is sought to be modeled by using only one or only a very few nonlinear three-dimensional (3D) beam elements with 6 degrees of freedom (DOF) at each of the 2 nodes of the element, and the nonlinear coupling of axial-torsional-bidirectional bending deformations is considered for each element. The effect of plasticity in each member is included using the mechanism of plastic hinges which may form at any point(s) along the length of each element or member. To make Direct Numerical Simulation of a micro-latticed cellular solid possible for its eventual applications, the tangent stiffness matrix for a spatial beam element undergoing large elastic-plastic deformation is explicitly derived using a Reissner-type mixed variational principle in the co-rotational updated Lagrangian reference frame. In order to avoid the inversion of the Jacobian matrix, a Newton homotopy method is employed to solve the tangent-stiffness equations. We are developing a code called CELLS/LIDS [CELLular Structures/Large Inelastic DeformationS] providing the capabilities to study the variation of the mechanical properties of the low-mass metallic cellular structures by changing their topology. Thus, due to the efficiency of this method we propose to employ it for topology optimization design, and for impact/energy absorption analyses of elastic-plastic micro-cellular structures, and then micro-architecting them for desired elastic-plastic properties.

The Resistance of Structural Elements to Impact and Shock-Wave Load

The ability of structural elements withstanding impact and shock-wave loading has been considered. The dynamic stress-strain state of structural elements at the stage of occurrence of large elastic-plastic deformation and fracture has been investigated, and different criteria of the structure strength has been used. The numerical and experimental results have been compared.

Fabrication and in Situ Scanning Electron Microscope Lithiation of Mechanically Robust 3D Architected Si-Cu Core-Shell Nanolattices

Silicon has been intensely studied as an anode material in Li batteries because of its high storage capacity. A major drawback is that Si suffers from mechanical degradation because of the large volumetric expansion during lithiation. Nano-structuring Si can alleviate the problem for each nanoscale element such as nanowires and nanoparticles [1, 2] because of the size-induced ductility and the availability of open space for Si to expand into. However, incorporating such nanoscale elements into device-sized electrodes is difficult. Si particles assembled using the traditional slurry method, which is designed for intercalation type electrodes, tend to lose contact with the surrounding binder after repeated lithiation and delithiation cycles [3]. Therefore, we propose 3D architected Si-Cu core-shell nanolattices as interconnected, binder-free Li-ion battery electrodes with the combined benefits of size-induced ductility, fast electron and ion transport, and mechanically robust structural geometries. To fabricate architected Si-Cu core-shell electrodes, a polymer nanolattice mold is first made from positive photoresist on a glass substrate covered by metal thin film via two-photon lithography. Cu is then electroplated into the mold, and free-standing solid Cu nanolattices are made by removing the remaining photoresist. Amorphous Si (a-Si) is then deposited over Cu by plasma-enhanced chemical vapor deposition (PECVD). The Si layer is ~250nm in thickness, and amorphous Si is used to reduce cracking due to anisotropic stress during Si expansion. For in situ battery testing, an electrochemical half-cell is built inside of a scanning electron microscope (SEM) using a lithium electrode and the nano-architected Si-Cu electrode. First, Li is brought into contact with Si-Cu nanolattices directly with an oxidized layer of Li2O on Li as a solid electrolyte, and a constant voltage bias is applied during electrochemical cycling. In situ observation shows that during the first lithiation a reaction front propagates from the top of the electrode where it is contacting solid Li2O electrolyte to the bottom as each lattice beam expands in volume and bows out. During delithiation, no clear reaction front is observed as the structure contracts in volume entirely. Si volume expansion is calculated to be about 200% yet the total expansion of the electrode structure is minimal with no cracks formed on the beams at a rate of 0.25C-1C. To better study how the electrode will be cycled in practical batteries where electrode is fully submerged in liquid electrolyte, 10wt% LiTFSI in P14TFSI ionic liquid electrolyte is used to connect the Li electrode and the Si-Cu lattices inside SEM. Cyclic voltammetry confirms the electrochemical reaction occurs between Si and Li. Galvanostatic discharge indicates a first cycle capacity of ~3000mAh/g normalized by the mass of Si, and post-lithiation imaging indicates a 250% Si volume expansion with no cracks observed. Coin cells with high Si loading are being fabricated and tested for long term cycling performance. To better understand the evolution of local stresses within the Si-Cu nanolattices, we apply the theory and numerical capability developed by Di Leo, et al [4] to model the a-Si shell lithiation. The fully-coupled diffusion-deformation theory accounts for transient diffusion of Li, large elastic-plastic deformations, and the effect of mechanical stress on the diffusion of Li. The simulation shows that the core-shell beam geometry and the plastic deformation of the lithiated Si help relieve stresses inside Si and at the Si-Cu interface. Interfacial delamination is unlikely because the calculated tolerable critical flaw size is much larger than the observed void size at the Si-Cu interface using a transmission electron microscope (TEM). Reference: Chan, C. K., Peng, H., Liu, G., McIlwrath, K., Zhang, X. F., Huggins, R. A., & Cui, Y. (2008). High-performance lithium battery anodes using silicon nanowires. Nature Nanotechnology, 3(1), 31–35.McDowell, M. T., Lee, S. W., Nix, W. D., & Cui, Y. (2013). 25th anniversary article: Understanding the lithiation of silicon and other alloying anodes for lithium-ion batteries. Advanced Materials, 25(36), 4966–4985.Cui, L.-F., Hu, L., Wu, H., Choi, J. W., & Cui, Y. (2011). Inorganic Glue Enabling High Performance of Silicon Particles as Lithium Ion Battery Anode. Journal of The Electrochemical Society, 158(5), A592-A596.Leo, C. V. Di, Rejovitzky, E. & Anand, L. (2015). Diffusion–deformation theory for amorphous silicon anodes: The role of plastic deformation on electrochemical performance. Int. J. Solids Struct. 67-68, 283–196.

Ultimate compressive strength of deteriorated steel web plate with pitting and uniform corrosion wastage

Steel structural members are likely exposed to corrosive environments, and thus corrosion is one of the dominant life-limiting factors of steel structures. Extensive studies on the effectsof pitting and uniform corrosion on the strength performance of steel structural members under a wide variety of loading conditions have been undertaken to assess the relationship between pitting corrosion intensity and residual strength. The aim of this study is to investigate the ultimate compressive strength characteristics of steel web plate elements with pit and uniform corrosion wastage. A series of ABAQUSnonlinear elastic-plastic large deformation finite element analyses are carried out on I-shapedsection steel girder models with varying pittingcorrosion intensities. Artificial pitting of different intensities is considered on the web plates and a uniform loading applied vertically on the upper flange section. The ultimate load-carrying capacity of deteriorated models with different levels of uniform thickness loss is also studied. The results are applied to assessing the ultimate compressive strength of web plates with different pitting corrosion intensities and a uniform loss thicknessby developing design formulae that represent the average loss thickness versus the ultimate load-carrying capacity.

Steady Flow of Incompressible Elastic-Plastic Medium in a Spherical Matrix at Variable Loads

In the framework of the model of large elastic-plastic deformations, the flow of the material in a spherical matrix at varying loads is examined. Simulation is carried out under the condition of steady elastic-plastic boundary. In order to find an exact solution the assumption of an ideal smoothness of the walls and incompressibility of the material is accepted.

Diffusion–deformation theory for amorphous silicon anodes: The role of plastic deformation on electrochemical performance

Amorphous silicon (a-Si) is a promising material for anodes in Li-ion batteries due to its increased capacity relative to the current generation of graphite-based anode materials. However, the intercalation of lithium into a-Si induces very large elastic–plastic deformations, including volume changes of approximately 300%. We have formulated and numerically implemented a fully-coupled diffusion–deformation theory, which accounts for transient diffusion of lithium and accompanying large elastic–plastic deformations. The material parameters in the theory have been calibrated to experiments of galvanostatic cycling of a half-cell composed of an a-Si thin-film anode deposited on a quartz substrate, which have been reported in the literature. We show that our calibrated theory satisfactorily reproduces the mechanical response of such an anode — as measured by the changes in curvature of the substrate, as well as the electrochemical response — as measured by the voltage versus state-of-charge (SOC) response.We have applied our numerical simulation capability to model galvanostatic charging of hollow a-Si nanotubes whose exterior walls have been oxidized to prevent outward expansion; such anodes have been recently experimentally-realized in the literature. We show that the results from our numerical simulations are in good agreement with the experimentally-measured voltage versus SOC behavior at various charging rates (C-rates).Through our simulations, we have identified two major effects of plasticity on the electrochemical performance of a-Si anodes:•First, for a given voltage cut-off, plasticity enables lithiation of the anode to a higher SOC. This is because plastic flow reduces the stresses generated in the material, and thus reduces the potential required to lithiate the material.•Second, plastic deformation accounts for a significant percentage of the energy dissipated during the cycling of the anode at low C-rates.Hence, plasticity can have either (a) a beneficial effect, that is, a higher SOC for a given voltage cut-off; or (b) a detrimental effect, that is significant energy dissipation at low C-rates.

Analysis of ductile–brittle competitive fracture criteria for tension process of 7050 aluminum alloy based on elastic strain energy density

To predict the damage and fracture of material accurately in the process of large elastic–plastic deformation, this paper proposed ductile–brittle competitive fracture criteria based on elastic strain energy density (ESED), which have been proved to competitively affect fracture behavior in the analysis of metal forming process. Additionally, the ductile fracture criterion is based on continuous damage mechanics (CDM) and the brittle fracture criterion is based on fracture mechanics (FM). The analyses of deformation damage and fracture for notched and unnotched tension specimens in complex stress states have been carried out by experiment and finite element method (FEM) using the ductile–brittle competitive fracture criteria. The results from analyses on damage evolution and fracture of FEM are in good agreement with the experimental ones. The law of ductile–brittle competitive fracture has been quantitatively proved to be effective in the process of metal deformation.