Phenomenological Damage Model Research Articles

Deformation and failure behavior of 2024-T42 sheet under impact loading

The deformation and failure behavior of 2024-T42 aluminum alloy sheet was investigated through a combined experimental-numerical method. Nine types of specimens were designed to cover a wide range of stress triaxialities and strain rates. Quasi-static and dynamic tests were carried out by electronic testing machine and split Hopkinson tensile bar respectively, and digital image correlation (DIC) method was introduced to measure the deformation. The phenomenological damage model GISSMO (generalized incremental stress state dependent damage model) and Johnson-Cook model were adopted to simulate all of the above tests and the load-displacement curves through numerical simulation were derived. An optimization method was developed to obtain all the model parameters by matching the load-displacement curves from simulation with those from tests by LS-OPT. Finally, drop weight tests and tensile tests of the central-hole plate were conducted. The applicability and accuracy of the damage models were verified by comparing the simulation results with the experiments, which indicates that GISSMO model predicts better the tests than the Johnson-Cook failure model.

Evaluation of Crashworthiness Using High-Speed Imaging, 3D Digital Image Correlation, and Finite Element Analysis

To promote the use of newhigh-strengthmaterials in the automotive industry, the evaluation of crashworthiness is essential, both in terms of finite element (FE) analysis aswell as validation experiments. Thiswork proposes an approach to address the crash performance through high-speed imaging combined with 3D digital image correlation (3D-DIC). By tracking the deformation of the component continuously, cracks can be identified and coupled to the load and intrusion history of the experiment. The so-called crash index (CI) and its decreasing rate (CIDR) can then be estimated using only one single (or a few) component, instead of a set of components with different levels of intrusion and crushing. Crash boxes were axially and dynamically compressed to evaluate the crashworthiness of TRIP-aided bainite ferrite steel and press-hardenable steel. Acalibrated rate-dependent constitutivemodel, and a phenomenological damage model were used to simulate the crash box testing. The absorbed energy, the plastic deformation, and the CIDR were evaluated and compared to the experimentally counterparts. When applying the proposed method to evaluate the CIDR, a good agreement was found when using CI:s reported by other authors using large sets of crash boxes. The FE analyses showed a fairly good agreement with some underestimation in terms of energy absorptions. The crack formation was overestimated resulting in too high a predicted CIDR. It is concluded that the proposed method to evaluate the crashworthiness is promising. To improve the modelling accuracy, better prediction of the crack formation is needed and the introduction of the intrinsic material property, fracture toughness, is suggested for future investigations and model improvements.

Response of thin walled transversely stiffened clamped circular plates under uniform impulsive loads

Paper presents numerical models based on detailed characterization of various uncoupled damage models in a finite element analysis (FEA) setup to assess large deformations and observed ductile fracture failure modes of fully clamped circular plates as well as transversely stiffened circular plates in cross stiffened configurations under uniform impulsive loads. The numerical schemes have been based on a detailed definition of the constitutive properties based on inverse FEA simulations of the uniaxial tension test for the calibration of material and failure parameters. Experiments have been conducted using two types of freshly prepared mild steel uniaxial tension test specimens covering the envisaged range of stress tri-axialities to establish the steel plate material and fracture characteristics necessary for the calibration of the presented phenomenological damage models. Published results based on extensive experimental works by various authors on response of thin walled clamped circular plates under transversely applied uniform air blast loads, manifesting in large plastic deformations, thinning and tearing under various ductile fracture modes, have been used in the performance assessment of presented numerical models and procedure, which incorporate different damage models including temperature effects due to plastic dissipation. Based on evaluated performance of the discussed failure models within the FEA setup, a hybrid damage model with a tri-axiality based two part ductile fracture locus has been proposed, which shows very good correlation with the published experimental results, presented in terms of non-dimensional parameters over a wide range of impulsive loading. The validated numerical setup using the proposed hybrid damage model has also been used to predict the effect of transverse cross stiffened configurations of flat bar stiffeners on large deformations and ductile fracture of clamped circular plates under transverse uniform impulsive blast loads, along with some key insights in the evolution of plastic zones and damage progression.

Evaluation of uncoupled ductile damage models for fracture prediction in incremental sheet metal forming

The formability limit in a typical incremental sheet forming (ISF) far exceeds the conventional estimate assuming necking failure. The material subjected to incremental forming fails by fracture. Although damage models have been used to correlate the failure in incremental forming, a detailed understanding of the failure mechanism spanning strain paths is not clear yet. In this work, three parts with varied shapes (hybrid five lobe, pyramid and variable wall angle conical frustum (VWACF)) were developed using ISF to cover a range of possible strain paths. The failure is predicted using established uncoupled phenomenological damage models. Damage models were calibrated for AA1050 aluminium sheet by the method of inverse approach using carefully designed tensile tests and FE simulations. Three different damage models were implemented as user subroutine in commercial software code, ABAQUS/Explicit and the results predicted were compared. The linear damage accumulation used to develop fracture locus under monotonic loading could not predict the failure limit in a benchmark single groove test. Therefore a non linear damage accumulation rule (NLDA) is implemented to simulate ISF. The parameters of the NLDA were calibrated from the single groove test. The fracture forming limits during ISF was established using circular grid analysis near the failure zone of the formed part. A good agreement can be found between the experimental observations and numerical predictions for fracture location and part height. It was observed that the overall predictive capability of Hosford Coulomb (HC) damage model is better among three damage models investigated for the given range of loading conditions. However all the three models under-predicted the experimental fracture strain measured in ISF. The possible explanation for the discrepancy is explored.

Large deformations and failure of clamped circular steel plates under uniform impulsive loads using various phenomenological damage models

Paper presents numerical models based on a detailed characterization of various uncoupled damage models in a finite element analysis (FEA) setup to assess their results and comparative performance in simulation of structural response and failure of clamped circular plates subjected to a wide range of uniform impulse loading. The significance of numerical modeling of ductile fracture in simulating the various observed modes of failure in steel structures under intense blast loading has also been presented along with an overview of various phenomenological damage models in the published domain. Numerical schemes presented in the paper are founded on a detailed and well-defined material model using mechanical uniaxial tension tests (UTT) and its inverse FEA simulations. Elaborate UTT experiments have been conducted to establish the mechanical strength and ductile fracture characteristics of a particular grade of mild steel for its usage in the calibration of the discussed damage models. Relative performance of various simple as well as complex phenomenological damage models in simulating/ predicting the experimentally observed structural response and different failure modes of fully clamped circular steel plates over a broad range of uniform impulsive loads has also been presented. Published results based on extensive experimental works by various authors on response of thin walled clamped circular plates under transversely applied uniform air blast loads, manifesting in plastic deformations of large magnitude, inception of thinning and tearing under various ductile fracture modes, have been utilized in the validation of the numerical model and procedure. Based on the evaluated performance of the discussed numerical models, a hybrid damage model adopted within the FEA setup has been proposed, demonstrating a very good correlation of numerical predictions with experiments. The validated FEA setup incorporating the calibrated hybrid damage model has further been gainfully utilized towards critical insights in the evolution of plastic deformations, progression of damage and their correlation with experimentally observed failure modes over a wide range of loading, involving varying stress states and tri-axiality.

Characterization of high-strength bolts and the numerical representation method for an efficient crash analysis

This paper presents novel insights of a numerical bolt representation approach taking into account damage and failure, suitable for large-scale models as in full vehicle crash simulations. Custom-built experimental equipment combined with digital image correlation enables observation of bolt failure behavior and its physical characteristics under tension, shear as well as combined loading. A fine-meshed model demonstrates the transferability of the physical properties to numerics including the associated restrictions. The experimental and numerical findings are used to develop an efficient substitute bolt model with high prediction accuracy that takes into account the bolt kinematics due to the thread via volume elements.An isotropic constitutive law with linear elastic and multilinear plastic progression supplemented by a phenomenological damage model depicts the bolt material behavior numerically.The observation of the bolt models under different tension and shear ratios provides new insights to the models accuracy which is assessed by an analytically failure envelope.

Determination and Verification of GISSMO Fracture Properties of Bolts Used in Radioactive Waste Transport Containers.

Transport containers for radioactive materials should withstand drop tests according to the regulations. In order to prevent a loss or dispersal of the internal radioactive materials in the drop tests, a tightening of the lid of the transport container should be maintained. The opening of the lid, due to the drop impact, might cause the dispersion of internal contents or a loss of shielding performance. Thus, it is crucial to predict damage to the fastening bolt and its fracture. In this study, the damage parameters of the fastening bolt were acquired, and its fracture was predicted using the generalized incremental stress state-dependent damage model (GISSMO), a phenomenological damage model. Since the dedicated transport container is large and heavy, various jigs that can simulate the fall of the container were designed, and the accuracy of fracture prediction was verified. Digital image correlation (DIC) was introduced for the accurate measurement of the displacement, and load–displacement data for tensile, shear, and combined loads were successfully acquired. Finally, the load–displacement curve of the finite element analysis (FEA) with GISSMO until the point of the bolt fracture was compared with the curve obtained from the experiment, where a good agreement was observed.

Damage degradation model of aeolian sand concrete under freeze–thaw cycles based on macro-microscopic perspective

At present, the existing freeze–thaw damage models are mostly phenomenological damage models that use macroscopic indicators as variables, and there is a lack of a multi-scale freeze–thaw damage model that combines the macroscopic and microscopic perspectives. In this study, eight types of aeolian sand concrete (ASC) at the aeolian sand replacement rates of 0%, 10%, 20%, 30%, 40%, 60%, 80%, and 100% were subjected to freeze–thaw cycle test. Comprehensive analysis and evaluation were done of the frost resistance durability of ASC from the dynamic elastic modulus at the macro-scale and the pore structure at the micro-scale. The evolution law of the freeze–thaw damage characteristics of ASC was studied from a macroscopic and microscopic perspective. The freeze–thaw damage degradation model for ASC was established by transforming the irreversible energy dissipation into cumulative fatigue damage, and the applicability and reliability of the model were verified from the macro and micro multi-scale perspectives. The findings indicate that the introduction of aeolian sand could inhibit and delay concrete damage and deterioration, thus reinforcing the frost resistance durability of concrete. The decrease in the percentage of gel pores and transition pores and the increase in the percentage of large pores deteriorate ASC in freeze–thaw cycles. Whereas, increasing the percentage of gel pores and transition pores and decreasing the percentage of large pores could reinforce the frost resistance of ASC. The damage evolution model can manifest the development law for freeze–thaw deterioration in ASC from the macroscopic and microscopic perspectives. The model can be used as the theoretical foundation for the application of ASC in cold regions.

Experimental and Numerical Impact Analysis of Automotive Bumper Brackets Made of 2D Triaxially Braided CFRP Composites.

The impact behavior of carbon fiber epoxy bumper brackets reinforced with 2D biaxial and 2D triaxial braids was experimentally and numerically analyzed. For this purpose, a phenomenological damage model was modified and implemented as a user material in ABAQUS. It was hypothesized that all input parameters could be determined from a suitable high-speed test program. Therefore, novel impact test device was designed, developed and integrated into a drop tower. Drop tower tests with different impactor masses and impact velocities at different bumper bracket configurations were conducted to compare the numerically predicted deformation and damage behavior with experimental evidence. Good correlations between simulations and tests were found, both for the global structural deformation, including fracture, and local damage entities in the impact zone. It was proven that the developed phenomenological damage models can be fully applied for present-day industrial problems.

A multi-scale fatigue–creep coupled damage model for steel structures under extreme cyclic loading and temperature

In order to compute the process from the damage accumulation to failure of steel structures under extreme cyclic loading and temperature, a multi-scale fatigue–creep damage model has been developed. Based on the balance of micro-crack number density theory, the multi-scale fatigue damage model has been established using generalized self-consistent method. In the fatigue damage model, the scatter of micro-crack length is expressed by two-parameter Weibull distribution and the interaction among micro-cracks has been studied. In turn, the multi-scale fatigue–creep damage model has been developed by considering the nonlinear coupling of fatigue damage and creep damage. The validity of the developed model has been verified by comparing the predicted damage evolution curves with experimental damage data. The developed model enables to more accurately study the fatigue degradation of steel structures than the phenomenological damage models. Fatigue–creep damage analysis on steel turbine blades under different extreme operating condition are performed using the developed model.

Failure damage mechanical properties of thoracic and abdominal porcine aorta layers and related constitutive modeling: phenomenological and microstructural approach.

Despite increasing experimental and analytical efforts to investigate the irreversible effects of arterial tissue failure, the underlying mechanisms are still poorly understood. The goal of this study was to characterize the failure properties of the intact wall and each separated layer (intima, media, and adventitia) of the descending thoracic and infrarenal abdominal aorta and to test the hypothesis that the failure properties of layer-separated tissue depend on the location of the aorta. To test this hypothesis, we performed uniaxial tests to study the mechanical behavior of both intact and layer-separated porcine aortic tissue samples taken from descending thoracic and infrarenal abdominal aorta until complete failure. The fracture stress is higher in the infrarenal abdominal aorta than in the equivalent descending thoracic aorta. It was also found that the extrapolation of the elastic mechanical properties from the physiological to the supra-physiological regime for characterizing the mechanical response of the aorta would be inappropriate. Finally, we report values of constitutive parameters using phenomenological and microstructural damage models based on continuum damage mechanics theory. The phenomenological damage model gives an excellent fit to the experimental data compared to the microstructural damage model. Although the fitting results of the phenomenological model are better, the microstructural models can include physically motivated aspects obtained from experiments.

Fatigue crack initiation prediction using phantom nodes-based extended finite element method for S355 and S690 steel grades

The assessment of fatigue crack initiation behavior of steel structures is essential and important especially to improve the application of high strength steel in construction. For a complete understanding of fatigue endurance, it is necessary to combine the phenomenological damage model with finite element numerical approach. In this paper, phantom nodes-based extended finite element method is used to predict the fatigue crack initiation of steel material, considering a prediction by XFEM of coupon tests made of steel grades S355 and S690. A user-defined fatigue damage initiation subroutine based on Smith, Watson, and Topper (SWT) damage model combined with non-linear isotropic/kinematic cyclic hardening model is implemented to predict fatigue crack initiation. The proposed method is successfully validated based on fatigue coupon test results of both steel grades, S355 and S690.

Rate dependent ductility and damage threshold: Application to Nickel-based single crystal CMSX-4

A phenomenological damage model is proposed to account for the strain rate dependency of the damaging processes at high temperature. Mechanical softening during tertiary creep and monotonic tension are modeled by an isotropic scalar internal variable D, whose evolution is described using a rate damage law dD/dt=⋯ governed by visco-plasticity and accounting for the enhancement by stress triaxiality. A novel rate sensitive damage threshold is introduced in order to reproduce the rate dependency of the onset of damaging processes. Damage evolution is coupled with the visco-plasticity model developed by the same authors for single crystal superalloys and accounting for microstructural evolution (like γ'-rafting and coarsening) in Desmorat et al. (2017). The curves presented in this article are identified at 1050 °C for the Ni base single crystal superalloy CMSX-4 but the proposed rate sensitive threshold modeling can be applied to other alloys showing a rate sensitive damage onset, as for example the single crystal superalloys MC2 but also the polycrystalline aggregate AD 730™.

High temperature characterization and material model calibration for hot stamping of AA7075 aluminium sheet

This paper presents an overview of the elevated temperature characterization of AA7075 aluminium sheet and calibration of a custom material model implemented in LS-DYNA. The plasticity characterization was performed by isothermal tensile testing while formability characterization was performed via isothermal Nakazima testing in a wide range of temperatures and strain rates. A special heat treatment path representative of the hot stamping was developed and applied in both series of tests. The material model included Hill’48 yield with a non-associated flow rule and phenomenological damage model similar to GISSMO but extended to cover non-isothermal conditions.

Experimental investigation and phenomenological modeling of hygrothermal effect on tensile fatigue behavior of carbon/epoxy plain weave laminates

The purpose of this paper is to study the hygrothermal effect on fatigue behavior of quasi-isotropic carbon/epoxy plain weave aerospace laminates containing artificial flaw under axial tension–tension loading. Dry and wet specimens were tested at tensile load-controlled cyclic loading with a stress ratio R = 0.1 and a load frequency of 7 Hz at room temperature (RT) and at 82℃ under different stress levels. Allowable stiffness change as a failure criterion was used to determine the delamination propagation onset threshold under cyclic tensile loading at each environmental condition. The delamination propagation onset was verified using the ultrasonic imaging (C-Scan) technique. The experimental results show that (1) fatigue life of CFRP specimens was more individually affected by moisture than by temperature and (2) combined moisture and temperature cause a drastic decrease in fatigue life. Finally, an investigation of the effect of hygrothermal conditions on stiffness degradation and damage of composite laminates subjected to tensile fatigue loading has been also carried. On the basis of the residual stiffness degradation, a damage variable was presented and phenomenological damage models were proposed by employing fatigue modulus and secant modulus concepts as measure of material damage.

Experimental fracture characterisation of an anisotropic magnesium alloy sheet in proportional and non-proportional loading conditions

A comprehensive experimental investigation was performed to characterize the fracture behaviour of a rare-earth magnesium alloy sheet, ZEK100-O, under both proportional and non-proportional loading conditions. This material possesses severe plastic anisotropy and tension-compression asymmetry that evolve with plastic deformation and is an excellent candidate to experimentally evaluate phenomenological fracture modelling strategies. Different types of specimen geometries were fabricated in different orientations with respect to the rolling direction of the sheet to reveal the anisotropic fracture response of the alloy. Moreover, three different types of plane-strain tension tests, namely, v-bend, butterfly, and Nakazima dome tests were conducted and compared in terms of their applicability for fracture characterization of sheet materials. To visualize directional dependency of the fracture response of the magnesium alloy, experimental fracture loci for different orientations were constructed. Furthermore, non-proportional tests were performed in which abrupt changes in stress state were imposed to study the role of the loading history on fracture behaviour of the alloy. The non-proportional tests entailed pre-straining the material in uniaxial and equi-biaxial tension up to a prescribed plastic work level, followed by extreme strain path changes to plane-strain tension and shear states. Non-proportional deformations with such severe strain path variations have not been reported in the literature for materials with complex anisotropic behaviour such as ZEK100-O. The results of which have enabled the direct experimental evaluation of phenomenological damage models without performing an inverse calibration from finite element simulations. Based on the results of the non-proportional tests, it was shown that simple damage indicators were unable to describe the influence of severe changes in the strain path on fracture.

Simulating toughness properties under varying temperatures with micromechanical and phenomenological damage models

The sustainable and efficient use of high-strength micro-alloyed steels is of particular interest in today’s industry. Using modern steels with high strength and excellent toughness enables thinner constructions, for example in infrastructure applications, for pressure vessels or pipelines. Sufficient toughness is of special importance to avoid catastrophic brittle failure. Yet, the simplified, conventional design rules prevent a full exploitation of the properties of modern high strength steels. Modern simulation models are able to represent the actual failure characteristics of high strength steels and thereby help to fully exploit the potential of these materials. To include toughness properties, it is essential that the models are able to describe the transition behavior of these steels. The materials’ behavior in the transition region is characterized by a competition of ductile and cleavage failure mechanisms. To simulate the corresponding behavior, it is necessary to adapt damage mechanics models for considering both effects. While numerous studies on the simulation of either ductile or cleavage failure exist, only a limited selection is available on investigations in the transition range. Therefore, the presented study investigates two representatives of the most popular groups of ductile failure models. The Gurson-Tvergaard-Needleman model (GTN) is investigated as a micromechanical model while the Modified-Bai-Wierzbicki model (MBW) is selected as a phenomenological model. Both are combined with the Orowan cleavage fracture model. Investigations are performed on a thermomechanical rolled S355, for which the cleavage fracture stress and the parameters for the ductile failure models were experimentally determined. The study compares simulations of Charpy impact toughness tests to experimental results to determine which model class delivers results that are more accurate. The focus of the investigation is hereby set on the simulation of the lower shelf and the lower transition area. In addition, the efficiency of the simulations performed is also evaluated.

Effect of nanosectioning on surface features and stiffness of an amorphous glassy polymer

Sectioning of a glassy polymer, poly(methyl methacrylate), at nanoscale was carried out by means of an ultramicrotome. The effects of sectioning thickness and speed on the morphology and stiffness over the sectioned surface were then investigated by atomic force microscopy. A critical sectioning thickness and speed were identified, below which flat and smooth surfaces were created with homogeneous elasticity. Above the critical thickness or speed, periodic localized structures formed on the sectioned surfaces, leading to a nonhomogeneous distribution of the mapped elasticity. Finite element simulation reproduced the periodic structures observed in the experiments. The influence of sectioning speed on the surface stiffness was predicted by a phenomenological damage model and was found to correlate with the experimental results. The study lends confidence that critical sectioning conditions (e.g., the sectioning thickness and speed) can be identified to avoid undesirable local deformation and damage in the manufacture of small scale optical and photonic components and devices. POLYM. ENG. SCI., 58:1849–1857, 2018. © 2017 Society of Plastics Engineers

Influence of Different Yield Loci on Failure Prediction with Damage Models

Advanced high strength steels are widely used in the automotive industry to simultaneously improve crash performance and reduce the car body weight. A drawback of these multiphase steels is their sensitivity to damage effects and thus the reduction of ductility. For that reason the Forming Limit Curve is only partially suitable for this class of steels. An improvement in failure prediction can be obtained by using damage mechanics. The objective of this paper is to comparatively review the phenomenological damage model GISSMO and the Enhanced Lemaitre Damage Model. GISSMO is combined with three different yield loci, namely von Mises, Hill48 and Barlat2000 to investigate the influence of the choice of the plasticity description on damage modelling. The Enhanced Lemaitre Model is used with Hill48. An inverse parameter identification strategy for a DP1000 based on stress-strain curves and optical strain measurements of shear, uniaxial, notch and (equi-)biaxial tension tests is applied to calibrate the models. A strong dependency of fracture strains on the choice of yield locus can be observed. The identified models are validated on a cross-die cup showing ductile fracture with slight necking.

Theoretical formulation of double scalar damage variables

The predictive utility of a damage model depends heavily on its particular choice of a damage variable, which serves as a macroscopic approximation in describing the underlying micromechanical processes of microdefects. In the case of spatially perfectly randomly distributed microcracks or microvoids in all directions, isotropic damage model is an appropriate choice, and scalar damage variables were widely used for isotropic or one-dimensional phenomenological damage models. The simplicity of a scalar damage representation is indeed very attractive. However, a scalar damage model is of somewhat limited use in practice. In order to entirely characterize the isotropic damage behaviors of damaged materials in multidimensional space, a system theory of isotropic double scalar damage variables, including the expressions of specific damage energy release rate, the coupled constitutive equations corresponding to damage, the conditions of admissibility for two scalar damage effective tensors within the framework of the thermodynamics of irreversible processes, was provided and analyzed in this study. Compared with the former studies, the theoretical formulations of double scalar damage variables in this study are given in the form of matrix, which has many features such as simpleness, directness, convenience and programmable characteristics. It is worth mentioning that the above-mentioned theoretical formulations are only logically reasonable. Owing to the limitations of time, conditions, funds, etc. they should be subject to multifaceted experiments before their innovative significance can be fully verified. The current level of research can be regarded as an exploratory attempt in this field.