Experimental and Numerical Failure Criteria for Sheet Metal Forming

For sheet metal forming, often the forming limit diagram (FLD) is used as failure criterion as it can be derived easily in experiments. It is based on the assumption that localization of strain in the sheet plane is responsible for crack initiation, but application of FLD is limited to linear strain paths. Hence, only forming processes with approximately the same deformation history as the experiments carried out for FLD determination should be evaluated by this criterion. Forming limit stress diagrams (FLSD) do not exhibit such strict limitations. They are based on the assumption that principal stresses in the sheet plane are responsible for crack initiation. As these stresses are usually calculated by FE analysis using elastic plastic material laws, strain hardening is considered. Two‐step forming tests as application examples prove the FLSD to be adequate for evaluation of non‐linear forming processes with alternating forming directions. Nevertheless, FLSD are derived in extensive investigations which makes them unattractive for most industrial applications. Furthermore, both FLD and FLSD do not consider the physical background of ductile crack initiation which is provoked by an interaction of local stress triaxiality and equivalent plastic strain. Hence, a reliable failure criterion should concentrate on these two parameters. The Gurson‐Tvergaard‐Needleman‐ (GTN‐) damage model can predict crack initiation during sheet metal forming. Application of the GTN model to 2 step forming tests with the bake hardening steel H220BD+Z showed good agreement to experimental results although a sensitivity of the model to mesh size and stress triaxiality is observed.     

Generalized, Three-Dimensional Definition, Description, and Derived Limits of the Triaxial Failure of Metals

Metal failure in many applications, such as ballistic impact, containment, shielding, metal forming, and crashworthiness, occurs while the material is in a three-dimensional state of stress. Many previous definitions of triaxiality use two invariants to define the relative stress state in a virtual element, leading to a characterization that can be better thought of as biaxial. In this paper, an additional parameter based upon the third stress invariant is defined, which extends the characterization of the state of stress to three dimensions and to true triaxiality. The relation of the two parameters is explored and limits are found in the failure surface, which is used in defining the critical failure regions. Standard tests are examined to determine if they can provide enough data to construct these regions of interest and new tests are proposed, which envelope the limits and thus define this failure surface.     

Optimal City-Center Takeoff Operation of Tiltrotor Aircraft in One Engine Failure

This paper investigates optimal tiltrotor flight trajectories and performance in vertical takeoff operations from a city-center heliport considering the possibility of one engine failure. A two-dimensional longitudinal rigid body model of a tiltrotor aircraft is used. Tiltrotor flights after engine failure in both continued takeoff and rejected takeoff are formulated as nonlinear optimal control problems that minimize the heliport size, subject to various constraints from safety considerations and tiltrotor performance limitations. These problems are parametrized via collocation into parameter optimization for numerical solutions. Extensive numerical solutions are obtained, and sensitivity analyses are conducted to examine effects of model parameter uncertainties. Optimization results indicate that the maximum gross weight capability of a tiltrotor in a vertical operation is determined by the need for safe landing in the event of a single engine failure. The height at which the decision for either continuing or rejecting the takeoff is made depends on the need to maintain sufficient height during the continued takeoff flight after an engine failure.     

金属薄板面内压剪变形的损伤断裂行为

相变诱导塑性钢（TRansformation induced plasticity, TRIP）作为常用的先进高强钢在汽车等交通工具的轻量化方面有广泛的应用前景。而对于其复杂零件的成形过程,韧性断裂是不可忽视的问题之一。本文针对现有实验装置不易诱发薄板承受面内压剪时断裂失效,从而无法研究板料负应力三轴度区间断裂行为的问题,以高强钢TRIP800薄板为研究对象,设计了可在单向试验机完成压剪实验的试样和夹具。通过调整夹具旋转角度和试样装夹位置可以实现同一种试样在广泛的负应力三轴度范围内进行压剪断裂分析。基于ABAQUS/Explicit平台建立了三个典型加载方向20°、30°和45°对应的压剪过程有限元模型,分析表明:三种情况的试样局部变形区域的应力三轴度都小于0且断裂点的应力三轴度低至?0.485,验证了设计的装置可实现负应力三轴度区间的断裂失效分析,同时基于MMC断裂准则分析了不同应力状态的初始损伤情况及损伤扩展路径。      

Simulated Micromechanical Models Using Artificial Neural Networks

A new method, termed simulated micromechanical models using artificial neural networks (MMANN), is proposed to generate micromechanical material models for nonlinear and damage behavior of heterogeneous materials. Artificial neural networks (ANN) are trained with results from detailed nonlinear finite-element (FE) analyses of a repeating unit cell (UC), with and without induced damage, e.g., voids or cracks between the fiber and matrix phases. The FE simulations are used to form the effective stress-strain response for a unit cell with different geometry and damage parameters. The FE analyses are performed for a relatively small number of applied strain paths and damage parameters. It is shown that MMANN material models of this type exhibit many interesting features, including different tension and compression response, that are usually difficult to model by conventional micromechanical approaches. MMANN material models can be easily applied in a displacement-based FE for nonlinear analysis of composite structures. Application examples are shown where micromodels are generated to represent the homogenized nonlinear multiaxial response of a unidirectional composite with and without damage. In the case of analysis with damage growth, thermodynamics with irreversible processes (TIP) is used to derive the response of an equivalent homogenized damage medium with evolution equations for damage. The proposed damage formulation incorporates the generalizations generated by the MMANN method for stresses and other possible responses from analysis results of unit cells with fixed levels of damage.     

Numerical Modelling of Toughness and Failure Processes in Steel Structures

The necessity to avoid failure of steel structures often results in conservative design as the load bearing capacity of structures cannot be quantified precisely with the common design tools mainly focussing on strength properties. Nevertheless, recent developments in mechanical and civil engineering show tendencies to an optimized utilization of the material properties. This requires improved understanding of failure behaviour and precise failure prediction tools. In this work, damage mechanics failure criteria and models are discussed which can be applied for failure prediction. For the Gurson‐Tvergaard‐Needleman (GTN) model, physical interpretations of the model parameters are presented which help for a reliable and reproducible failure prediction. Procedures for parameter quantification are demonstrated as well. In the second part, examples for successful application of damage models to industrial problems are presented. Ductile crack initiation during offshore laying of pipelines is simulated in large scale bending tests and predicted quantitatively both with the GTN model and with damage curves, and a numerical prediction of physical upper shelf crack initiation values is shown. A correlation between size distributions of voids on ductile fracture surfaces and adequate FE mesh size is suggested to overcome the mesh size sensitivity of the GTN model. Finally, the complex failure behaviour of multiphase steels with cleavage and ductile failure appearances is simulated numerically by coupling of the GTN model and the Cohesive Zone model.     

Measurement of Epoxy Resin Tension, Compression, and Shear Stress–Strain Curves over a Wide Range of Strain Rates Using Small Test Specimens

The next generation aircraft engines are designed to be lighter and stronger than engines currently in use by using carbon fiber composites. In order to certify these engines, ballistic impact tests and computational analyses must be completed, which will simulate a “blade out” event in a catastrophic engine failure In order to computationally simulate the engine failure, properties of the carbon fiber and resin matrix must be known. When conducting computer simulations using a micromechanics approach, experimental tensile, compressive, and shear data are needed for constitutive modeling of the resin matrix material. The material properties of an Epon E862 epoxy resin will be investigated because it is a commercial 176°C (350°F) cure resin currently being used in these aircraft engines. These properties will be measured using optical measurement techniques. The epoxy specimens will be tested in tension, compression and torsional loadings under various strain rates ranging from 10?5?to?10?1?s?1 and temperatures ranging from room temperature to 80°C. To test the specimens at high temperatures, a specialized clear temperature chamber was used. The results show that the test procedure developed can accurately and quickly categorize the material response characteristics of an epoxy resin. In addition, the results display clear strain rate and temperature dependencies in the material response.     

A New Damage Evolution Model for Cold Forging of Bearing Steel-Balls

As ductile damage has a severe impact on the performance of bearing steel-balls (BSB), it is necessary to apply the ductile damage evolution model for predicting the distribution of ductile damage in BSB. A new ductile damage model was developed using physically-based internal state variables method by considering the effect of two important stress state parameters: stress triaxiality and relative ratio of max principal tension stress, on the ductile damage evolution. The newly developed ductile damage model was implemented into the commercial FE code, DEFORM-3D, via a user defined subroutine and cold forging simulation was operated. BSB formation tests were carried out and the microstructure and micro-damage were examined from the tested samples. FE simulation results of ductile damage were compared with those of tested samples. Good agreements have been achieved, which proves that the newly developed ductile damage model enables micro-damage evolution during cold forging to be well predicted. Some constructive suggestions have been obtained to improve the quality of BSB during cold forging.     

Camage leading to ductile fracture under high strain-rate conditions

Quantitative metallographic studies of damage evolution leading to ductile fracture under high strainrate loading conditions are presented. A model material is considered, namely, leaded brass, which contains a dispersed globular lead phase that acts as void nucleation sites. Interrupted tensile split Hopkinson bar tests have been performed to capture the evolution of porosity and void aspect ratio with deformation at strain rates up to 3000 s⁻¹. Both uniaxial and notched specimen geometries were considered to allow the effects of remote stress triaxiality to be investigated. Plate impact testing has also been performed to investigate the evolution of damage under the intense tensile triaxiality and extremely high rates of deformation (10⁵ s⁻¹) occurring within a spall layer. Quantitative metallographic measurements of damage within deformed specimens are used to assess predictions from a Gursonbased constitutive model implemented within an explicit dynamic finite element code. A stresscontrolled void nucleation treatment is shown to capture the effect of triaxiality on damage initiation for the range of experiments considered. J.P. FOWLER, formerly Research Associate with the Mechanical and Aerospace Engineering Department, Carleton University This article is based on a presentation given in the symposium entiled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Damage leading to ductile fracture under high strain-rate conditions

Quantitative metallographic studies of damage evolution leading to ductile fracture under high strain-rate loading conditions are presented. A model material is considered, namely, leaded brass, which contains a dispersed globular lead phase that acts as void nucleation sites. Interrupted tensile split Hopkinson bar tests have been performed to capture the evolution of porosity and void aspect ratio with deformation at strain rates up to 3000 s⁻¹. Both uniaxial and notched specimen geometries were considered to allow the effects of remote stress triaxiality to be investigated. Plate impact testing has also been performed to investigate the evolution of damage under the intense tensile triaxiality and extremely high rates of deformation (10⁵ s⁻¹) occurring within a spall layer. Quantitative metallographic measurements of damage within deformed specimens are used to assess predictions from a Gurson-based constitutive model implemented within an explicit dynamic finite element code. A stress-controlled void nucleation treatment is shown to capture the effect of triaxiality on damage initiation for the range of experiments considered. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Simulation of shear plugging through thin plates using the GRIM Eulerian hydrocode

Ballistic experiments have been performed using aluminum spheres against 10-mm rolled homogenous armour (RHA), MARS270, MARS300, and titanium alloy plates to investigate the influence of the plugging mechanism on material properties. The experiments have measured the threshold for plug mass and velocity as well as the recovered aluminum sphere mass over a range of velocities. Some of the experiments have been simulated using the in-house second generation Eulerian hydrocode GRIM. The calculations feature advanced material algorithms derived from interrupted tensile testing techniques and a triaxial failure model derived from notched tensile tests over a range of strain rates and temperatures. The effect of mesh resolution on the results has been investigated and understood. The simulation results illustrate the importance of the constitutive model in the shear localization process and the subsequent plugging phenomena. The stress triaxiality is seen as the dominant feature in controlling the onset and subsequent propagation of the crack leading to the shear plug. The simulations have demonstrated that accurate numerics coupled with accurate constitutive and fracture algorithms can successfully reproduce the observed experimental features. However, extrapolation of the fracture data leads to the simulations overpredicting the plug damage. The reasons for this are discussed. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II”, held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Simulation of shear plugging through thin plates using the GRIM eulerian hydrocode

Ballistic experiments have been performed using aluminum spheres against 10-mm rolled homogenous armour (RHA), MARS270, MARS300, and titanium alloy plates to investigate the influence of the plugging mechanism on material properties. The experiments have measured the threshold for plug mass and velocity as well as the recovered aluminum sphere mass over a range of velocities. Some of the experiments have been simulated using the in-house second generation Eulerian hydrocode GRIM. The calculations feature advanced material algorithms derived from interrupted tensile testing techniques and a triaxial failure model derived from notched tensile tests over a range of strain rates and temperatures. The effect of mesh resolution on the results has been investigated and understood. The simulation results illustrate the importance of the constitutive model in the shear localization process and the subsequent plugging phenomena. The stress triaxiality is seen as the dominant feature in controlling the onset and subsequent propagation of the crack leading to the shear plug. The simulations have demonstrated that accurate numerics coupled with accurate constitutive and fracture algorithms can successfully reproduce the observed experimental features. However, extrapolation of the fracture data leads to the simulations overpredicting the plug damage. The reasons for this are discussed. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials—Part II,” held during the 1998 Fall TMS/ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees.     

Gouging and Fracture of Engine Containment Structure under Fragment Impact

This paper presents a numerical study of the failure response of an aircraft engine containment panel obliquely impacted by a titanium turbine fragment. A three-branch Bao-Wierzbicki fracture criterion is first calibrated for the target material (2219-T851 aluminum alloy) by performing tensile tests on round bars and upsetting tests on short cylinders. With this fracture model, the finite-element simulation of the impact test successfully captures the formation of an indentation/gouging channel on the proximal surface of the panel and the growth of a crack on the distal surface. An extensive parametric study is conducted on the effect of fracture criteria, mesh size, projectile pitch angles, and finite-element codes. Deficiencies of the Johnson-Cook and the constant critical strain fracture model are identified. It is found that the numerically predicted residual thickness and mass loss of the panel are sensitive to the magnitude of the pitch angle of the projectile. A large difference in calculated energy dissipation between ABAQUS and LS-DYNA is observed.     

Methodology for Impact Modeling of Triaxial Braided Composites Using Shell Elements

In this paper, a two-dimensional triaxial braided composite model has been studied using the nonlinear explicit finite-element code LSDYNA. The unit cell consists of six subcells and material properties associated with shell element integration point simulate braiding architecture. The local material properties were selected by correlation of the global behavior of a coupon model with static specimen tests. By changing subcell size and orientation angle at integration points, different braids architectures were obtained. Panel ballistic models were performed with benefits of computation efficiency of shell elements. Mechanical properties, panel impact threshold velocities, and failure initiations for braids with bias angles of 75, 60, 45, and 30° were studied. Boundary effects were also investigated.     

Simplified Braiding through Integration Points Model for Triaxially Braided Composites

A simplified methodology has been developed for modeling two-dimensional triaxially braided composite plates impacted by a soft projectile using an explicit nonlinear finite-element analysis code LS-DYNA. The fiber preform architecture is modeled using shell elements by incorporating the fiber preform architecture at the level of integration points. The soft projectile was modeled by an equation of state. An arbitrary Lagrangian–Eulerian formulation is used to resolve numerical problems caused by large deformation of the projectile. The computed results indicate that this numerical model is able to simulate a triaxially braided composite undergoing a ballistic impact effectively and accurately, including the deformation and failure with a reasonable level of computational efficiency.     

Nonlinear Analysis of Masonry Arches Strengthened with Composite Materials

The nonlinear behavior of masonry arches strengthened with externally bonded composite materials is investigated. A finite-element (FE) formulation that is specially tailored for the nonlinear analysis of the strengthened arch is developed. The FE formulation takes into account material nonlinearity of the masonry construction and high-order kinematic relations for the layered element. Implementation of the above concept in the FE framework reduces the general problem to a one-dimensional nonlinear formulation in polar coordinates with a closed-form representation of the elemental Jacobian matrix (tangent stiffness). A numerical study that examines the capabilities of the model and highlights various aspects of the nonlinear behavior of the strengthened masonry arch is presented. Emphasis is placed on the unique effects near irregular points and the nonlinear evolution of these effects through the loading process. A comparison with experimental results and a discussion of the correlating aspects and the ones that designate needs of further study are also presented.     

Damage accumulation and failure of HY-100 steel

Strain-induced damage accumulation in the form of void volume fractions and number densities has been experimentally characterized for an HY-100 steel subjected to tensile failure over a range of temperatures (−85 °C to 25 °C), strain rates (10⁻³/s to 10³/s), and stress states (stress triaxiality ratios of 0.8 to 1.3). While the strain-induced evolution of damage is relatively insensitive to temperature and strain rate, it increases very rapidly with increasing stress triaxiality. In particular, the large body of void-growth data presented suggests the presence of an initially slow void-growth stage that can be described by a relationship with a form similar to that predicted by Rice and Tracey (but with increased dependence on stress triaxiality). The damage results also indicate a transition to rapid void growth (and imminent coalescence by a void-sheet mechanism) at a critical void volume fraction that decreases slowly with an increasing stress triaxiality ratio. A straightforward analysis, based on the experimental observations, relates the observed experimental dependence of failure strains on stress triaxiality for this steel.     

The influence of tensile stress states on the failure of HY-100 steel

The failure of an HY-100 steel plate has been examined as a function of stress state using notched and un-notched axisymmetric tensile specimens. The results show that increasing stress triaxiality leads to a rapid decrease in failure strains in a manner that is exponentially dependent on the degree of triaxiality. Two ductile failure mechanisms are identified: a void coalescence process, in which relatively equiaxed voids grow to impingement, and a void-sheet process, which links by a shear instability process large, elongated inclusion-initiated voids. The void-sheet mechanism intervenes and limits ductility at high-stress triaxialities in transversely oriented HY steel plate material, whereas the former process controls failure in longitudinally oriented material. These orientation effects are related to the morphology and alignment of the nonmetallic inclusion stringers that act as the primary void nucleation sites. Calcium treatments for inclusion-shape control improve ductility, especially at intermediate-stress triaxialities, primarily by suppressing the local conditions which give rise to the void-sheet instability process.     

An eulerian finite-element model for determination of deformation state of a copper subjected to orthogonal cutting

An Eulerian finite-element (FE) model was developed to predict the stress and strain distributions in the material subjected to the orthogonal machining process. Metallographic sections taken from commercially pure copper samples and subjected to orthogonal cutting were examined to determine the local strain gradients generated in the material ahead of the cutting tool tip. Local flow stress values were estimated from the microhardness measurements. Experimental flow stress and equivalent plastic strain values were found to obey a Voce-type exponential relationship, which was used in the development of the material model for the numerical simulations. The sizes of both the primary deformation zone (350 μm) and the secondary deformation zone (50 μm) predicted by the numerical model were in agreement with the experimental observations. The experimental results showed that the equivalent strain was 3.65 in the material 50 μm directly ahead of the tool tip, which compared well with the numerically observed strain (3.50). According to the numerical observations, along the primary shear plane, the high tool tip stress of 410 MPa decreased to 260 MPa near the chip root. Numerical and experimental stress and strain distributions correlated well in terms of both magnitudes and distributions, indicating that the application of an Eulerian FE approach served to predict the deformation state of the material ahead of the tool tip successfully.