Damage Growth Law Research Articles

Mesoscopic unit cell analysis of ductile failure under plane stress conditions

Ductile failure under plane stress conditions is analyzed at the meso-scale using periodic unit cell model simulations of void growth in a plastically deforming matrix. Equivalent strains to failure by the onset of plastic instability at the macro-scale are estimated using the loss of ellipticity criterion for the equilibrium equations. Failure loci obtained from the cell model simulations are compared with the predictions of an instability-based ductile failure model and the Hosford–Coulomb damage indicator model, under both proportional and non-proportional loading conditions. The instability-based model is shown to quantitatively predict the shape of the failure locus under proportional loading, including the presence of a cusp at uniaxial tension and a ductility minimum under plane strain tension, in the absence of heuristic adjustable parameters in the failure criterion. It is shown that the characteristic shape of the plane stress failure locus is primarily due to the Lode dependence of the failure criterion, and not the damage growth law as assumed in the damage indicator models. Under non-proportional loading involving a step change in loading direction at an intermediate strain, the instability-based model correctly predicts the non-linear variation of the failure strain as a function of the intermediate strain; unlike a linear variation predicted by the damage indicator models, which is not in agreement with the cell model simulations. Forming limit curves showing the strains to the onset of localized necking in thin sheets are also obtained from the cell model simulations using an appropriate modification of the macroscopic instability criterion.

Morphological and damage growth characteristics of shell-type damage of fused silica optics induced by ultraviolet laser pulses.

Under the radiation of a nanosecond pulse laser, the types of damage and damage profile of fused silica optics are closely related to the surface and subsurface defects of the component. Using the raster-scanning mode to measure the laser-induced damage threshold of fused silica optics, three different types and sizes of damage patterns are found, of which shell damage is the intermediate state and is a bridge connecting submicrometer-size damage and catastrophic damage. This paper mainly studies the mechanism and damage growth law of shell damage, analyzes the model of laser-induced shell damage, and discusses the probability and cause of shell-damage growth.

A non-linear ductile damage growth law at elevated temperature

Continuum damage mechanics (CDM) model is commonly used for the prediction of ductile fracture. For numerical simulation of ductile fracture in impact or high-temperature problems, the damage growth law that incorporates the effect of high temperature is needed. Experimentally, it has been observed that damage growth decreases with temperature. However, the damage growth law at high temperature is not easily available in the literature. In the present work, a damage growth law at high temperature is proposed for steel, based on the experimental measurement of damage carried out at IIT Kanpur.

Nanosecond laser-induced surface damage and material failure mechanism of single crystal CaF2 (111) at 355 nm

Surface damage and material failure mechanism of CaF2 single crystal by 355 nm/6.8 ns laser pulses are systematically studied in this work. Surface damage characteristics, such as damage threshold, damage growth threshold, damage growth laws and damage growth coefficient of CaF2 crystal are carefully studied. Surface material cracking and local material vitrification (from CaF2 crystal to defective CaF2-x materials) are revealed. Material decomposition, oxidation and formation of Ca0, Ca2+and (F−-F−) centers in surface layer are illustrated. Laser-driven thermal accumulation and thermal-stress gradient in CaF2 crystal are calculated and discussed based on the theory of Fourier heat conduction and thermal-elastic constitutive equations. Theory analysis suggests that the material failure process in CaF2 crystal is mainly driven by significant thermal stress gradient. Thermal gradient induce the material decomposition and local vitrification in CaF2 crystal. Combined results on surface damage and material failure behavior are beneficial to understand nanosecond laser-driven modifications and damage in fluoride crystals at ultraviolet wavelength.

A nonlinear CDM based damage growth law for ductile materials

A nonlinear ductile damage growth criterion is proposed based on continuum damage mechanics (CDM) approach. The model is derived in the framework of thermodynamically consistent CDM assuming damage to be isotropic. In this study, the damage dissipation potential is also derived to be a function of varying strain hardening exponent in addition to damage strain energy release rate density. Uniaxial tensile tests and load-unload-cyclic tensile tests for AISI 1020 steel, AISI 1030 steel and Al 2024 aluminum alloy are considered for the determination of their respective damage variable D and other parameters required for the model(s). The experimental results are very closely predicted, with a deviation of 0%–3%, by the proposed model for each of the materials. The model is also tested with predictabilities of damage growth by other models in the literature. Present model detects the state of damage quantitatively at any level of plastic strain and uses simpler material tests to find the parameters of the model. So, it should be useful in metal forming industries to assess the damage growth for the desired deformation level a priori. The superiority of the new model is clarified by the deviations in the predictability of test results by other models.

Simulation of Fracture in the Taylor Test Using Continuum Damage Mechanics Model

Impact problems lead to dynamic fracture and the study of this fracture is always a challenge. Impact problems are characterized by large plastic deformation, high strain rates and thermal softening. The strain rate regime of 103s−1 and beyond is generally regarded as the high strain rate range where the strain rate and thermal effects become important and need to be considered. The effects of high temperature and high strain rate on the fracture patterns in Taylor rod of IS2062: 2006 GR E410W A steel are studied by using the developed damage growth law at high temperature and high strain rate based on continuum damage mechanics model. The stress and strain fields are obtained by using the commercial finite element software ABAQUS/Explicit where the damage growth law (at high temperature/strain rate) is incorporated through an external user defined material subroutine (VUMAT). The critical damage criterion is used to predict the fracture initiation. After that, the spread of fracture is simulated by tracing the path of the failed elements.

Ductile Behaviour Characterization of Low Carbon Steel: a CDM Approach

In this paper, the ductile behaviour of two different low carbon steels, C-Mn-440 and interstitial free high strength (IFHS), is presented using a continuum damage mechanics (CDM) approach. The damage growth law is adopted to predict the ductile response of the specified materials. Cyclic load-unload tensile tests in combination with standard uniaxial tensile tests helped to estimate the necessary parameters: damage variable, D, fracture stress, σf, threshold damage strain, e0, and strain hardening exponent, n, required to apply the model. The strain hardening exponent estimated from the cyclic test data is used to predict the damage variable, D. Increase of damage shows deterioration of the hardening exponent magnitudes varying nonlinearly. The simulated flow curve by the damage variable, D, corresponding to the loadunload test is observed to approximate the experimental true stress-true strain curve very closely up to the onset of necking for both the materials. The experimental values of D, as obtained for C-Mn-440 and IFHS steels, vary from 0.10 to 0.44 and 0.09 to 0.45, respectively. The critical damage parameters, DC, for the considered materials are 0.44 and 0.45, representing their good ductile response.

Damage measurements via DIC

The present paper is devoted to the measurement of damage by resorting to image correlation techniques. This full-field measurement procedure gives access to 2D and 3D displacements that can be utilized to analyze damage mechanisms, to estimate damage fields, and to determine material parameters of damage growth laws. Different features associated with image correlation are addressed in the context of continuum damage mechanics. Applications concerning damage detection, damage quantification and damage model validation are presented.

A nonlinear ductile damage growth law

One of the commonly used approaches for the prediction of ductile fracture is the continuum damage mechanics model, in which the void density is represented by a continuum variable called damage. For the prediction of fracture, an evolution law for the void growth, called the damage growth law, is needed. As per the continuum thermodynamics framework, the damage growth law is obtained from some proposed expression for the damage potential. The damage growth laws reported in the literature, based on some proposed expressions for the damage potential, have played a useful role in predicting fracture initiation in some engineering materials. However, some of them do not agree with the experimental trends of damage growth in other engineering materials. In almost all the laws, while expressing the material constants in terms of the measurable quantities in tension test, the triaxiality is assumed constant which does not happen after the necking. In the present work, an expression for the damage potential is proposed that leads to a nonlinear ductile damage growth law for steel. The material constants of the damage growth law are determined from the experimental measurement of void growth as well as triaxiality at various plastic strain levels in tension test conducted at IIT Kanpur. Thus, it avoids making any assumption about the triaxiality. It is shown that this law is consistent with the trends of damage growth of some other experimental results reported in the literature.

A discrete damage zone model for mixed-mode delamination of composites under high-cycle fatigue

A discrete damage zone model is developed to describe the mode-mix ratio and temperature dependent delamination of laminated composite materials under high cycle fatigue loading within the framework of the finite element method. In this approach, discrete nonlinear spring elements are placed at the finite element nodes of the laminate interface, and a combination of static and fatigue damage growth laws is used to define its constitutive behavior. The model is implemented in the commercial software Abaqus using the user element subroutine. The static damage model parameters are estimated from fracture mechanics principles, whereas the fatigue damage model parameters are calibrated by fitting the numerical results to published experimental data. A quadratic relation is proposed to describe the non-monotonic variation of fatigue damage model parameters with mode-mix ratio. Next, an Arrhenius relation is proposed for the temperature dependence of fatigue damage, in addition to the incorporation of the temperature dependence of critical fracture energy. The model is convergent upon mesh refinement; however, for accurate prediction the mesh size used for model calibration should be sufficiently small. The model predicted fatigue crack growth rates are in agreement with those obtained from a quadratic relation for the Paris law parameters for variable mode mix conditions, thus verifying the approach. While the model captures the temperature effects on delamination for mode I and 50 % mode II, our prediction deviates from experiments for pure mode II, since the corresponding damage mechanism entirely changes with temperature.

Multiscale approach to predict crack initiation in unidirectional off-axis laminates

Crack initiation in unidirectional off-axis laminates made of carbon fiber and epoxy resin is predicted based on multiscale modeling. This multiscale modeling consists of two finite-element analyses (FEA) on different scales. One is macroscopic FEA, based on the assumption of homogeneous materials, and the other is microscopic periodic unit-cell (PUC) analysis using a micromechanical model. The macroscopic FEA is performed by applying uniaxial tension to off-axis laminates, in which we employ an anisotropic elasto-plastic constitutive law to obtain accurate deformation fields in laminates. In the microscopic PUC analysis, the strain history at a point in laminates obtained from the macroscopic FEA is applied as external forces, and crack initiation is predicted using two failure criteria for the matrix resin. The first is the dilatational energy density criterion under elastic deformation, and the second is a ductile damage growth law under plastic deformation. The simulated predictions are compared with the experiments results.

A nonlinear CDM model for ductile failure analysis of steel bridge columns under cyclic loading

A nonlinear cyclic plasticity damage model for ductile metals, which is able to take large deformation effects into consideration, has been developed using a new damage dissipation potential formulation in order to predict the cyclic inelastic behavior of steel bridge piers. The cyclic constitutive equations that employ the combined isotropic---kinematic hardening rule for plastic deformation is incorporated into the damage mechanics in conjunction with the large strain formulation. The damage growth law is based on the experimental observations that the evolution of microvoids results in nonlinear damage accumulation with plastic deformation. The damage model parameters and the procedure for their identification are presented. The proposed model has been validated and successfully applied to thin-walled steel bridge tubular columns subjected to alternating lateral displacements to evaluate the seismic performance.

Experimental comparison of damage performance induced by nanosecond 1 laser between K9 and fused silica optics

The initial damage threshold, the damage growth threshold and the damage growth laws of K9 glass and fused silica glass are tested respectively in the same experimental condition with 1 nanosecond laser. The comparison of the laser induced damage performance between the two glass materials is performed. The results show that the initial damage thresholds of the two glass materials are the same, the damage area growths both obey the exponential increase rule and their damage depth growths obey the linear increase rule. However, there is apparent difference in the rule of damage growth. For example, the damage growth threshold is lower and the damage growth coefficient is higher for K9 glass. This can be explained by the difference in the material mechanical strength between the two glass materials. The present research is very important for choosing transparent optical materials used in high power laser.

Numerical analysis of damage for prediction of fracture initiation in deep drawing

The sheet metal may have inherent voids/imperfections present because of preprocessing. These voids/imperfections grow under the applied load resulting into final fracture. The occurrence of ductile fracture is often a limiting factor in metal forming processes. Prediction of the initiation of ductile fracture allows a prior modification of the process which can result in a defect-free final product with financial savings. The intensity of voids is often represented by introducing a variable called damage. This paper deals with the prediction of fracture initiation in deep drawn cup using Lemaitre's continuum damage mechanics model. The damage is incorporated in the constitutive equation through the principle of strain equivalence. The damage is evaluated using the damage growth law proposed by Lemaitre. An in-house 3D finite element formulation is employed for the analysis. The maximum cup height at which the fracture initiates is determined using the critical damage criterion. A parametric study of the maximum cup height is carried out to investigate the influence of material, geometric and other process parameters.

DUCTILE FAILURE SIMULATION IN SPHERODIZED STEEL USING A CONTINUUM DAMAGE MECHANICS COUPLED FINITE ELEMENT FORMULATION

Ductile fracture occurs due to microvoid nucleation, growth and, finally, coalescence into microcracks. These microcracks grow in the presence of stresses leading to fracture. In this work, a criterion based on this phenomenon is used to simulate ductile fracture in a class of steel specimens. A critical value of the damage variable, estimated from experimental results, is used as an indicator of fracture initiation. A continuum damage mechanics model is employed to incorporate the damage in the constitutive relation of the material. A damage growth law based on experimental results is used. It is observed that the damage reaches the critical value first at the center in both the cylindrical and prenotched specimens. Thus, the failure begins at the center and then grows radially outward toward the free surface. The analysis is carried out till the damage reaches the critical value across the whole cross-section, at which point the specimen is considered to have failed.

Numerical simulation of fracture in cup drawing

Prediction of the initiation of ductile fracture in deep drawing allows a prior modification of the process which can result in a defect-free final product. This paper deals with the prediction of fracture initiation in deep drawn cup using Lemaitre’s continuum damage mechanics model. The damage is incorporated in the constitutive equation through the principle of strain equivalence. The damage is evaluated using the damage growth law proposed by Lemaitre. An in-house 3D finite element formulation is employed for the analysis. Finite element formulation is based on updated Lagrangian approach. Logarithmic strain measure is used. The incremental stress is made objective by evaluating it in a frame rotating with the material particle. The material is assumed to be elasto-plastic with isotropic strain hardening using von Mises yield criterion. Modified Newton-Raphson iterative technique is used to solve the nonlinear incremental equations. The fracture location predicted by the present formulation is in agreement with the results reported in the literature.

Effect of thermal stresses on fused silica surface on the laser induced damage

To study the effect of the thermal stresses on the optics, experiment is performed to measure the damage threshold of the two fused silica samples with one annealed to eliminate thermal stresses while the other not. The measurement includes the effects of the thermal stresses on the initial damage threshold of the fused silica, the damage growth threshold, and the damage growth laws. The results show that the damage threshold decreases as the thermal stresses increase, and the damage induced by the laser is accelerated by the thermal stresses. For the same laser intensity, the damage growth factor is higher for the area with higher thermal stresses, but the damage growth still obeys the exponential increase rule and no obvious effect of the thermal stresses is found on the damage growth threshold. The study here will determine to some extent whether the technology of the CO2 laser pretreatment can be applied to the large-aperture optics or not.

Structural health monitoring – What is the prescription?

Structural health monitoring (SHM) systems can prevent structural failure of safety-critical structures such as aircraft, bridges, nuclear reactors and dams, which cannot be allowed to fail. An SHM system uses the techniques of non-destructive inspection (NDI) to provide continuous (or on-demand) information about the state of a structure, so that an assessment of the structural integrity can be made at any time, and timely remedial actions may be taken as necessary. A large number of sensors forms the front end of an SHM system to provide information on the condition of the structure. The information from the sensors is incorporated into structural analyses and failure models to assess the state of the structure and to predict the remaining lifetime. Thus, the underlying concept is based on detecting and characterizing damage and assessing it in terms of failure mechanics and damage growth laws. Materials engineering and applied mechanics play dominant roles in both the diagnostic and prognostic components of SHM. A probabilistic approach is essential, as will be shown by an example of the growth and detection, or lack thereof, of surface-breaking cracks. The probabilistic approach also plays a key role in the determination of inspection schedules.

Digital Image Mechanical Identification (DIMI)

A continuous pathway from digital images acquired during a mechanical test to quantitative identification of a constitutive law is presented herein based on displacement field analysis. From images, displacement fields are directly estimated within a finite element framework. From the latter, the application of the equilibrium gap method provides the means for rigidity field evaluation. In the present case, a reconditioned formulation is proposed for a better stability. Last, postulating a specific form of a damage law, a linear system is formed that gives a direct access to the (non-linear) damage growth law in one step. The two last procedures are presented, validated on an artificial case, and applied to the case of a biaxial tension of a composite sample driven up to failure. A quantitative estimate of the quality of the determination is proposed, and in the last application, it is shown that no more than 7% of the displacement field fluctuations are not accounted for by the determined damage law.

A continuum damage mechanics model for ductile fracture

Continuum damage mechanics theory together with large deformation elastic–plastic finite element analysis has been used to predict crack growth initiation in ductile materials. The damage growth law is based on experimental observations reported in the literature. A local crack growth initiation criterion is proposed. The criterion makes use of the critical damage as the continuum parameter and the average austenite grain size as the characteristic length. To test the validity of this criterion, experiments have been conducted on standard specimens and have also been simulated numerically. The proposed criterion has been used to predict the values of the critical load at crack growth initiation and the fracture toughness. The numerically predicted values compare favourably with the experimental values.