Evaluation of Ductile Damage Parameters under High Stress Triaxiality

The GTN model proposed by Gurson, Tvergaard and Needleman has been widely applied to predict ductile fracture. However, the evaluation of the GTN model under high stress triaxiality has only been reported in a few studies. In this paper, a series of tensile tests on round notched specimens were performed to evaluate the applicability of the GTN model parameters under high stress triaxiality. The evaluation was carried out by comparing the predicted load-displacement curves with experimental results. It was observed the GTN model parameters only depend on the material except the critical void volume fraction. The influence of stress triaxiality on the critical void volume fraction was discussed. A further discussion about the construction of a new void coalescence criterion for the GTN model was also presented in this paper.     

Determination of Ductile Damage Parameters by Local Deformation Fields: Measurement and Simulation

This work comprises the development, implementation and application of methods for the parameter identification of damage mechanical constitutive laws. Ductile damage is described on a continuum mechanical basis by extension of the von Mises yield condition with the Gurson–Tvergaard–Needleman as well as with the Rousselier model. The classical Rousselier model is complemented by accelerated void growth and void nucleation. The non-linear boundary and initial value problem is solved by the finite element system SPC–PMHP, which was developed in the frame of the special research program SFB393 for parallel computers. The material parameters are identified by locally measured displacement fields and measured force–displacement curves. For the material parameter identification a non-linear optimization algorithm is used, which renders the objective function to a minimum by means of a gradient based method. A useful strategy to identify the material parameters was found by careful numerical studies. Finally, using the object grating method the local displacement fields as well as the force–displacement curves are measured at notched flat bar tension specimens made of StE 690 and the parameters of the material are identified.     

金属基复合材料和强度与损伤分析

用观察计算力学的方法分析了金属基复合材料（ＭＭＣ）多重损伤与强度的关系,采用唯象的内聚力模型模拟纤维／基体界面的脱粘和采用Ｇ－Ｔ模型描述韧性基体的损伤。并用上述模型分析了长纤维增强ＭＭＣ在横向荷载作用下损伤演化的规律,讨论了不同界面性质与材料强度及损伤、破坏模式之间的关系。     

Experimental investigations and modeling of volume change induced by void growth in polyamide 11

Polymers are known to be sensitive to hydrostatic pressure. The influence of stress triaxiality ratio on cavitation and damage has been highlighted in numerous studies. This paper proposes experimental investigations allowing the control of both the stress triaxiality ratio and the void distribution via microscopic observations of microtome-cut surfaces from interrupted tests. With the help of a finite element code, the Gurson–Tvergaard–Needleman model was calibrated by using these multi-scale experimental data. Then comparison between both numerical and analytical models and experimental data was performed. Bridgman formulae were reported to be valid up to the peak load. Moreover, a better understanding of the time evolution of significant parameters such as the porosity (volume change) and the stress triaxiality ratio (hydrostatic pressure), was highlighted.     

Effects of microscale inertia on dynamic ductile crack growth

The aim of this paper is to investigate the role of microscale inertia in dynamic ductile crack growth. A constitutive model for porous solids that accounts for dynamic effects due to void growth is proposed. The model has been implemented in a finite element code and simulations of crack growth in a notched bar and in an edge cracked specimen have been performed. Results are compared to predictions obtained via the Gurson–Tvergaard–Needleman (GTN) model where micro-inertia effects are not accounted for. It is found that microscale inertia has a significant influence on the crack growth. In particular, it is shown that micro-inertia plays an important role during the strain localisation process by impeding void growth. Therefore, the resulting damage accumulation occurs in a more progressive manner. For this reason, simulations based on the proposed modelling exhibit much less mesh sensitivity than those based on the viscoplastic GTN model. Microscale inertia is also found to lead to lower crack speeds. Effects of micro-inertia on fracture toughness are evaluated.     

Extension of the gurson model accounting for the void size effect

A continuum model of solids with cylindrical microvoids is proposed based on the Taylor dislocation model.The model is an extension of Gurson model in the sense that the void size effect is accounted for. Beside the void volume fraction f, the intrinsic material length I becomes a parameter representing voids since the void size comes into play in the Gurson model. Approximate yield functions in analytic forms are suggested for both solids with cylindrical microvoids and with spherical microvoids. The application to uniaxial tension curves shows a precise agreement between the approximate analytic yield function and the “exact” parametric form of integrals.     

A penny-shaped cohesive crack model for material damage

A novel micromechanics based damage model is proposed to address failure mechanism of defected solids with randomly distributed penny-shaped cohesive micro-cracks (Barenblatt–Dugdale type). Energy release contribution to the material damage process is estimated in a representative volume element (RVE) under macro hydrostatic stress state. Macro-constitutive relations of RVE are derived via self-consistent homogenization scheme, and they are characterized by effective nonlinear elastic properties and a class of pressure sensitive plasticity which depends on crack opening volume fraction and Poisson’s ratio. Several distinguished features of the present model are compared with Gurson model and Gurson–Tvergaard–Needleman (GTN) model, showing that the proposed model can better capture material degradation and catastrophic failure due to cohesive micro-crack growth and coalescence.     

MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW MASS-DAMPING

These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low mass and damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined mass-damping parameter (low m^*ζ), or a high mass-damping (highm^*ζ ). For our low m^*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm^*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the mass-damping (m^*ζ), whereas the regime of synchronization (measured by the range of velocity U^*) is dependent primarily on the mass ratio, m^*ζ. At low (m^*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of mass ratios (m^*=1–20), when plotted against (m^*+C_A) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m^*+C_A)ζ 0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m^*+C_A) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (f_N), to form a normalized velocity (U^*/f^*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratiosm^* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m^*.     

Ductile fracture of materials with high void volumefraction

In the present paper, axisymmetric cell models containing one or two voids and athree-dimensional cell model containing two voids have been used to investigate void size andspacing effect on the ductile fracture in materials with high initial void volume fraction. They areperformed for round smooth and round notched specimens under uniaxial tension. The examplematerial used for comparison is a nodular cast iron material GGG-40 with initial void volumefraction of 7.7%. The parameters considered in this paper are void size and shape foraxisymmetric cell models containing a single void, and void distribution pattern foraxisymmetric and 3D cell models containing two voids of different sizes. The results obtainedfrom these cell models by using FEM calculations are compared with the Gurson model, theGurson–Tvergaard–Needleman model, the Rice–Tracey model and the modified Rice–Traceymodel. It can be stated that the influence of void size and void spacing on the growth in volumeof voids is very large, and it is dependent on the distribution of voids. Using non-uniform voiddistribution, the results of axisymmetric cell models can explain how a void can grow in anunstable state under very low stress triaxiality at very small strain as observed in experiments.Calculations using cell models containing two voids give very different results about the stableand unstable growth of voids which are strongly dependent on the configuration of cell model.     

Relations between a micro-mechanical model and a damage model for ductile failure in shear

Gurson type constitutive models that account for void growth to coalescence are not able to describe ductile fracture in simple shear, where there is no hydrostatic tension in the material. But recent micro-mechanical studies have shown that in shear the voids are flattened out to micro-cracks, which rotate and elongate until interaction with neighbouring micro-cracks gives coalescence. Thus, the failure mechanism is very different from that under tensile loading. Also, the Gurson model has recently been extended to describe failure in shear, by adding a damage term to the expression for the growth of the void volume fraction, and it has been shown that this extended model can represent experimental observations. Here, numerical studies are carried out to compare predictions of the shear-extended Gurson model with the shear failures predicted by the micro-mechanical cell model. Both models show a strong dependence on the level of hydrostatic tension. Even though the reason for this pressure dependence is different in the two models, as the shear-extended Gurson model does not describe voids flattening out and the associated failure mechanism by micro-cracks interacting with neighbouring micro-cracks, it is shown that the trends of the predictions are in good agreement.     

Modeling stress state dependent damage evolution in a cast Al–Si–Mg aluminum alloy

Internal state variable rate equations are cast in a continuum framework to model void nucleation, growth, and coalescence in a cast Al–Si–Mg aluminum alloy. The kinematics and constitutive relations for damage resulting from void nucleation, growth, and coalescence are discussed. Because damage evolution is intimately coupled with the stress state, internal state variable hardening rate equations are developed to distinguish between compression, tension, and torsion straining conditions. The scalar isotropic hardening equation and second rank tensorial kinematic hardening equation from the Bammann–Chiesa–Johnson (BCJ) Plasticity model are modified to account for hardening rate differences under tension, compression, and torsion. A method for determining the material constants for the plasticity and damage equations is presented. Parameter determination for the proposed phenomenological nucleation rate equation, motivated from fracture mechanics and microscale physical observations, involves counting nucleation sites as a function of strain from optical micrographs. Although different void growth models can be included, the McClintock void growth model is used in this study. A coalescence model is also introduced. The damage framework is then evaluated with respect to experimental tensile data of notched Al–Si–Mg cast aluminum alloy specimens. Finite element results employing the damage framework are shown to illustrate its usefulness.     

A mesomechanical approach to inhomogeneous particulate composites undergoing localized damage:: part I—a mesodomain simulation

This paper presents a mesoscale homogenization methodology to deal with the damage localization in inhomogeneous particulate-reinforced composites. An effective local particle volume fraction, f ^v_loc,eff, which includes the particle size effect is suggested to characterize the damage-inducing aspect of clusters. The clustering regions in a particulate composite accommodating the saturated local damage at an applied stress amplitude are simulated by mesodomains, subdomains of homogeneous medium and homogeneous damage distribution. The size of the mesodomains is determined by the transition condition from local damage to global damage via macro-mechanics. The mesodomain positions are found in a materials science manner by mapping the area contours of f ^v_loc,eff for the composite. Transformation of a clustering composite into a two-homogeneous phase material enables one to appropriately illustrate the local constitutive behaviours, and paves the way to predict saturated local damage life.     

On the extension of the Gurson-type porous plasticity models for prediction of ductile fracture under shear-dominated conditions

One of the major drawbacks of the Gurson-type of porous plasticity models is the inability of these models to predict material failure under low stress triaxiality, shear dominated conditions. This study addresses this issue by combining the damage mechanics concept with the porous plasticity model that accounts for void nucleation, growth and coalescence. In particular, the widely adopted Gurson–Tvergaard–Needleman (GTN) model is extended by coupling two damage parameters, representing the volumetric damage (void volume fraction) and the shear damage, respectively, into the yield function and flow potential. The effectiveness of the new model is illustrated through a series of numerical tests comparing its performance with existing models. The current model not only is capable of predicting damage and fracture under low (even negative) triaxiality conditions but also suppresses spurious damage that has been shown to develop in earlier modifications of the GTN model for moderate to high triaxiality regimes. Finally the modified GTN model is applied to predict the ductile fracture behavior of a beta-treated Zircaloy-4 by coupling the proposed damage modeling framework with a recently developed J₂–J₃ plasticity model for the matrix material. Model parameters are calibrated using experimental data, and the calibrated model predicts failure initiation and propagation in various specimens experiencing a wide range of triaxiality and Lode parameter combinations.     

A constitutive model for elastoplastic solids containing primary and secondary voids

In many ductile metallic alloys, the damage process controlled by the growth and coalescence of primary voids nucleated on particles with a size varying typically between 1 and 100 μm, is affected by the growth of much smaller secondary voids nucleated on inclusions with a size varying typically between 0.1 and 3 μm. The goal of this work is first to quantify the potential effect of the growth of these secondary voids on the coalescence of primary voids using finite element (FE) unit cell calculations and second to formulate a new constitutive model incorporating this effect. The nucleation and growth of secondary voids do essentially not affect the growth of the primary voids but mainly accelerate the void coalescence process. The drop of the ductility caused by the presence of secondary voids increases if the nucleation strain decreases and/or if their volume fraction increases and/or if the primary voids are flat. A strong coupling is indeed observed between the shape of the primary voids and the growth of the second population enhancing the anisotropy of the ductility induced by void shape effects. The new micromechanics-based coalescence condition for internal necking introduces the softening induced by secondary voids growing in the ligament between two primary voids. The FE cell calculations were used to guide and assess the development of this model. The use of the coalescence condition relies on a closed-form model for estimating the evolution of the secondary voids in the vicinity of a primary cavity. This coalescence criterion is connected to an extended Gurson model for the first population including the effect of the void aspect ratio. With respect to classical models for single void population, this new constitutive model improves the predictive potential of damage constitutive models devoted to ductile metal while requiring only two new parameters, i.e. the initial porosity of second population and a void nucleation stress, without any additional adjustment.     

On strain and damage interactions during tearing: 3D in situ measurements and simulations for a ductile alloy (AA2139-T3)

Strain and damage interactions during tearing of a ductile Al-alloy with high work hardening are assessed in situ and in 3D combining two recently developed experimental techniques, namely, synchrotron laminography and digital volume correlation. Digital volume correlation consists of registering 3D laminography images. Via simultaneous assessments of 3D strain and damage at a distance of 1-mm ahead of a notch root of a thin Compact Tension-like specimen, it is found that parallel crossing slant strained bands are active from the beginning of loading in a region where the crack will be slanted. These bands have an intermittent activity but are stable in space. Even at late stages of deformation strained bands can stop their activity highlighting the importance of plasticity on the failure process rather than damage softening. One void is followed over the loading history and seen to grow and orient along the slant strained band at very late stages of deformation. Void growth and strain are quantified. Gurson–Tvergaard–Needleman-type simulations using damage nucleation for shear, which is based on the Lode parameter, are performed and capture slant fracture but not the initial strain fields and in particular the experimentally found slant bands. The band formation and strain distribution inside and outside the bands are discussed further using plane strain simulations accounting for plastic material heterogeneity in soft zones.     

Damage of ductile materials deforming under multiple plastic or viscoplastic mechanisms

This work presents a model to represent ductile failure (i.e. failure controlled by nucleation, growth and coalescence) of materials whose irreversible deformation is controlled by several plastic or viscoplastic deformation mechanisms. In addition work hardening may result from both isotropic and kinematic hardening. Damage is represented by a single variable representing void volume fraction. The model uses an additive decomposition of the plastic strain rate tensor. The model is developed based on the definition of damage dependant effective scalar stresses. The model is first developed within the generalized standard material framework and expressions for Helmholtz free energy, yield potential and dissipation potential are proposed. In absence of void nucleation, the evolution of the void volume fraction is governed by mass conservation and damage does not need to be represented by state variables. The model is extended to account for void nucleation. It is implemented in a finite element software to perform structural computations. The model is applied to three case studies: (i) failure by void growth and coalescence by internal necking (pipeline steel) where plastic flow is either governed by the Gurson–Tvergaard–Needleman model or the Thomason model, (ii) creep failure (Grade 91 creep resistant steel) where viscoplastic flow is controlled by dislocation creep or diffusional creep and (iii) ductile rupture after pre-compression (aluminum alloy) where kinematic hardening plays an important role.