Rate-dependent Damage Research Articles

A rate-dependent damage mechanics model for predicting plasticity and ductile fracture behavior of sheet metals at high strain rates

Uniaxial tensile tests were performed on H340 steel sheets at different strain rates (10-4 to 103s-1) and temperatures (–30 °C and 280 °C). Oscillation-free forces were measured during high-speed tests at strain rates of up to 1000 s-1 using specimens with different stress states. Material hardening curve, strain rate sensitivity, temperature effects, and Taylor-Quinney coefficient for adiabatic temperature calculations were determined in experiments. Digital image correlation (DIC) technique was employed to measure displacement, deformation, and local strain fields. Meanwhile, the temperature fields of specimen gauge section were measured with a high–speed thermal camera in the uniaxial tensile tests at various strain rates. Damage and fracture-related parameters were calibrated and validated using porosity measurements on SEM micrographs and in combination with finite element (FE) simulations. A rate– and temperature–dependent plasticity and damage mechanics model (e2MBW) was proposed and calibrated to predict the plasticity and fracture behavior of H340 under different loading speeds. The study demonstrated good agreement in the overall experimental and simulated force–displacement responses and local strain evolution across all fracture specimens at loading speeds from 0.005 mm/s to 10000 mm/s.

Rate-dependent damage and failure behavior of lithium-ion battery electrodes

The mechanical properties and failure behavior of composite electrodes are critical to understanding the internal short circuits and ensuring the crush safety of lithium-ion batteries used in electric transportation. This study provides a comprehensive experimental investigation into the strain rate–dependent tensile/compressive behavior and failure mechanism of both anode and cathode, covering a range from quasi-static to dynamic conditions. A universal testing machine equipped with an industrial camera was used to assess the mechanical properties and observe the deformation process of the electrodes under quasi-static conditions. Additionally, a split Hopkinson bar system, coupled with a high-speed camera, was utilized to evaluate the mechanical properties and capture the deformation process of the electrodes under dynamic loading. The detailed deformation and failure modes of the electrodes were revealed by a combination of post-mortem characterization and images from high-speed cameras. The experimental results demonstrate a significant strain rate effect on the tensile and compressive mechanical behavior and failure mechanism of both anode and cathode. The rate dependence of tensile/compressive strength and failure strain were discussed, and the underlying mechanism for strain rate sensitivity was analyzed. The results and conclusions from this study provide an important foundation for the detailed modeling and failure prediction of lithium-ion batteries under impact loading. Further, these findings facilitate the safety design of electric vehicles by informing to enhance crash safety.

A viscoelastic-viscoplastic damage model with a cohesive zone in between

The present research sheds light on a first viscoelastic-viscoplastic damage model with a cohesive zone in between, implemented in finite element method. The viscoelastic layer, and viscoplastic layer were developed individually, which were then combined. The damage evolution was then observed, taking into account the rate-dependent behaviors. Three damage evolutions were possible, which are ‘viscoelastic-viscoplastic coupled damage, viscoelastic rate-dependent damage, and viscoplastic rate-dependent damage’. It was found during damage that the failure of one layer may be understood through the micromechanics of another layer, and that the work of separation was dependent on interfacial strength. The cohesive zone was thus observed as separated zone, and deformed zone. The separated zone signified viscoelastic activity, while the deformed zone signified viscoplastic activity. It was shown that the developed model may evolve as a function of measured properties. The model is capable of performing extensive dimensionless parametric studies. This finds application in biomedical science, structural engineering, materials design, among others.

Rate-dependent damage sequence interaction model for predicting the mechanical property of in-service aluminum alloy 6005A-T6

Engineering structures and materials will undergo fatigue, aging, and other degradation behaviors during long-term service under the combined influence of complex boundary conditions. These service damages make the materials and structures no longer meet the initial design requirements and pose a potential risk to the service system. This study proposes a material mesoscopic model to decouple the microstructure into a system composed of matrix and void phases. The matrix phase has an invariant constitutive relationship as an ideally undamaged material, and the different evolutionary behaviors of the void phase are described as damage evolution functions and lead to different stress–strain behaviors of the actual material. First, the damage described by different definitions is proposed, and a nonlinear function of damage evolution consistent with the Weibull distribution characteristic of microstructural continuity is derived. Then, an experimental–numerical method is improved to accurately identify the accelerated damage evolution behavior under various strain rates. Finally, the ideally undamaged constitutive of the matrix phase and the damage evolution function of the void phase are established, which can cover the void nucleation, growth, and aggregation process. Besides, the damage sequence interaction model is established in conjunction with the mesoscopic physical mechanism, and the total damage evolution function for materials containing prior service damage in subsequent ductile deformation is achieved by measuring the apparent elastic modulus of the material only. Finally, the ideally undamaged constitutive and damage evolution function are calibrated for aluminum alloy 6005A-T6, commonly used in the car body structure of rail vehicles, and verified with damaged specimens that experienced certain service loads. The material's damage sequence interaction mode is determined, and the rate-dependent residual strength is predicted.

A gradient-extended thermomechanical model for rate-dependent damage and failure within rubberlike polymeric materials at finite strains

Rate-dependencies play a crucial role in the mechanical response of polymeric materials. Besides viscoelasticity, many polymers also show pronounced rate-dependent behaviour with respect to damage accumulating within the material. Furthermore, thermal effects and large deformations have to be taken into account when modelling the mechanical behaviour of polymers. Within this work, we propose a novel fully thermomechanically coupled material model for the description of rate-dependent damage combined with viscoelasticity at finite strains. The model is based on the multiplicative decomposition of the deformation gradient into thermal and mechanical parts as well as a further decomposition of the mechanical part into equilibrium and non-equilibrium contributions. To describe the temporal dependencies of the damage evolution, we make use of a Perzyna-type approach. We furthermore show the thermodynamically consistent derivation of stresses and heat sources which arise due to energy dissipations triggered by the inelastic effects within the material. With the given material formulation, we are able to describe both, damage due to creep and due to relaxation in a precise manner. Besides the theoretical aspects, we describe the numerical implementation into finite element software and present numerical studies demonstrating the capabilities of the given model.

Rate dependent compressive failure and delamination growth in multidirectional composite laminates

A novel intralaminar model has, for the first time, been applied and validated for the rate-dependent failure of multidirectional carbon/epoxy laminates. Quasi-static compressive failure is evaluated by the growth of intralaminar rate-dependent damage combined with the interaction of cohesive zones for interlaminar delamination. A special feature of the intralaminar model is the homogenised ply response, allowing simultaneous damage-degradation of the polymer matrix combined with the fibres. To model the observed quasi-brittle failure response of the plies under finite deformation, we have used a viscoelastic-viscoplastic matrix combined with damage and isotropic hardening behaviour. Elastic transverse isotropy is used to model the fibre reinforcement of the plies. Standard cohesive surfaces are used to model the initiation and propagation of delamination. Numerical simulations using ABAQUS/Explicit are performed to predict the growth and delamination of intralaminar damage under compression in different laminates with 56 plies of IM7/8552 carbon/epoxy. Predictions of stress versus strain and damage growth are shown to agree well with experimental results for a range of strain rates and stacking sequences.

Stress softening of nanoparticle-crosslinked hydrogels described using a physics-based damage model

Despite the promising applications of hydrogels, their poor mechanical properties still greatly limit their further applications. To improve the mechanical properties of hydrogels, various strategies have been proposed. Hydrogels with nanoparticle-crosslinked polymer networks show excellent toughness, self-recovery, and other advantages, and thus have great prospects for use in tissue engineering, artificial muscles, flexible electronics, and other fields. There have been experimental and theoretical studies of its damage. However, the underlying microscale physical mechanisms have not been fully elucidated. Herein, we established a physics-based constitutive model to describe the mechanical behavior of nanoparticle-crosslinked hydrogels under cyclic loading. The deformation-induced damage and the rate-dependent damage were explained by the network alteration and kinetics of chain dissociation/association, respectively. The kinetics dissociation/association theory was modified considering the polymer chains that wind around nanoparticles. The Mullins stress softening and recovery during cyclic loading were described. Cyclic loading tests on nanoparticle-crosslinked hydrogels were carried out to verify the proposed constitutive model. It is demonstrated that the model can well describe the mechanical behavior of nanoparticle-crosslinked hydrogels during cyclic loading.

A dynamic description of the smoothing gradient damage model for quasi-brittle failure

Quasi-static simulations are of limited interest because cracks, if they are not severely constrained, propagate dynamically. When natural disasters such as earthquakes or explosions happen, structures made of quasi-brittle or brittle materials can suffer from failures activated by, for instance, loading at a high rate. Dynamic fractures, especially dynamic crack branching, are often observed during those events. We present in this paper, for the first time, a dynamic description of the smoothing gradient-enhanced damage model towards the simulation of quasi-brittle failure localization under time-dependent loading conditions. We introduce two efficient rate-dependent damage laws and various equivalent strain formulations to analyze the complicated stress states and inertia effects of dynamic regime, enhancing the capability of the adopted approach in modeling dynamic fracture and branching. The study is carried out using low-order finite elements, and the merits of the developed approach are examined through our numerical experiments, including mixed-mode fracture and dynamic crack branching simulations.

Rate-dependent damage evolution and crack branching of pipe under internal gaseous detonation loading

A rate-dependent damage evolution law was derived based on the thermally activated motion of dislocations. By writing the VUMAT subroutine, it was implemented to simulate the dynamic crack propagation and branching of pipe due to internal gaseous detonation. Also, the fluid-structure coupling between detonation wave and pipe was well achieved through immersed boundary method and “softened” contact formula. The predicted fracture profiles and pressure history inside the pipe were validated with experiments and compared with available results in literatures. Results demonstrated that the developed numerical model was more accurate in predicting the dynamic crack behaviors, especially the crack branching position relative to the main crack tip. The simulated average crack speed ranged from 171 m/s to 228 m/s, which well fell within the experimental range. Instead of dramatically decreasing, the speed of branched crack was comparable to that of the main crack. The damage field around the crack tip can reflect the direction of crack propagation or branching. The maximum strain rate always appeared at the right front of crack tip regardless of the subsequent crack behavior. It was further revealed that the high strain rate contributed to the straight propagation of crack, while branching was primarily governed by the particular strain pattern around the crack tip.

Gradient-extended damage modelling for polymeric materials at finite strains: Rate-dependent damage evolution combined with viscoelasticity

While the strong rate-dependent effects of polymeric materials in the elastic regime are well studied, the time-dependent effects that arise in the inelastic damage regime are still difficult to model and are therefore the subject of investigation. In this work, we propose a simple but flexible formulation for the description of rate-dependent damage combined with viscoelasticity at finite strains. This model is based on a finite viscoelastic material formulation combined with a Perzyna-type approach to describe the damage evolution equation. With this formulation we are able to describe both damage due to creep and relaxation of the polymer matrix in both a qualitative and quantitative manner. Besides the main aspects of thermodynamic consistency, we describe the numerical implementation into finite elements and present numerical examples to demonstrate the capabilities of the proposed model. At last, we compare the model with experimental data and show the good predictive capabilities of this newly developed material model.

Mesh objectivity in dynamic fracture analyses with rate dependent continuum damage models

This paper is aimed at investigating the mesh objectivity in dynamic fracture analyses employing strain rate dependent damage evolution as the localization limiter. Specifically, the goal is investigating and understanding the limits of applicability across various loading rates. For this purpose, dynamic fracture of a brittle material is simulated using a rate dependent scalar damage model. Dynamic fracture scenarios under a wide range of loading rates are considered, which yield various fracturing patterns ranging from localized to branched/diffused. The rate dependent damage model is seen to yield mesh objective predictions only at higher loading rates, which correspond to branched/diffused fractures. Results are not mesh objective at lower loading rates, which correspond to localized fractures. The regularization effect, at higher rates, is due to an intrinsic length-scale induced by the rate dependent damage law, and is related to the strain rate sensitivity parameter. For these cases, the predicted fracture patterns consist of thickened damage bands, spanning multiple element widths, and are wider than the intrinsic length-scale induced by the model. Thus, this feature can be viewed as a physical manifestation of the intrinsic length-scale. Wave propagation and dispersion in a one-dimensional version of the present damage model is analyzed further to explain the results. It is demonstrated that the group and phase velocity are finite and approach the elastic wave speed at higher loading rates, helping retain mesh objectivity. However they approach infinity at lower loading rates, causing the regularizing effect to vanish. Thus, the rate dependent damage model does not yield mesh objective results across all loading rates, and must be employed with caution.

A thermodynamically consistent viscoelastic with rate-dependent damage constitutive model

In this paper, a thermodynamically consistent viscoelastic and rate-dependent continuum damage constitutive model is proposed under small-deformation assumption. The model is consistent with quasi-static loading case that it is able to reproduce correct static strength when loading rate approaches to 0 by introducing a so-called pseudo damage state variable ϖ. In addition, the model can present increasing strength and strain at failure with increasing strain rate. The evolution of the pseudo damage state variable is described as a rate form of power of effective stress, while the damage state variable is given by a viscosity-like rate form equation. The viscoelastic behavior is described by the classic Prony series. Finally, the paper provides uniaxial tension, tension of plate-with-hole, and tension of particle-reinforced heterogeneous material as numerical examples to show viscoelastic behavior and damage development process.

Direct embedment of RVE-based microscale into lab size coupons to research fracture process in unidirectional and bidirectional composites

The structural applicability of fibre-reinforced polymer (FRP) composites requires testing for their resilience against fracture. The paper presents a virtual tool to configure the microscale geometrical model constituting the representative volume element embedded in the homogeneous macroscale region, providing an alternative to the tedious experimental procedures. The conformal meshing strategies in the microregion are also elucidated in the paper. The microscale model is enriched with the constitutive material models exhibiting complex phenomena of individual constituents of the composite and cohesive damage properties. The elastoplastic and elastic–viscoplastic material models coupled with the energy-based and rate-dependent damage initiation criteria, respectively, are applied to the matrix. At the same time, the fibre-matrix interface is treated with the weak traction–separation law. Through the virtual tool, the microscale region allows to make an insightful study of the toughness mechanism and visualise the damage initiation and propagation in the FRP structure at different fracture modes.

Dynamic crack penetration vs. deflection at material interfaces and the role of rate dependent strength and toughness

This work presents a numerical investigation into the dynamic crack penetration vs. deflection at a material interface, for materials exhibiting strain rate dependent damage evolution. The rate dependence of damage manifests as an increased strength and fracture energy (or toughness) at higher strain rates. For this purpose, a strain rate dependent continuum damage mechanics (CDM) based model is considered, which scales the material point softening damage law as a function of the strain rate. The investigations consider two materials, viz. the bulk and the interface, both modeled via the foregoing rate dependent damage model. Attention is focused on a mode I dynamic bulk crack impinging the interface at right angles, for the case where the interface is more strain rate sensitive than the bulk. The model is calibrated and validated with experimental data, and found to predict well the penetration/deflection behavior of a dynamic crack at an interface. Despite this, the predicted crack trajectory approaching the specimen boundary appears to be affected in some cases. The model is then used to conduct a sensitivity analysis for a wide range of bulk and interface properties (moduli, strengths, and fracture energy). The analyses reveal that dynamic crack impingement at the interface is accompanied by sharp changes in the local strain rates, thus altering the local bulk and interface strengths and toughnesses. So, a weak interface can become stronger and tougher than the bulk, locally and instantaneously, if it exhibits a higher strain rate sensitivity than the bulk. This implies that when damage evolution is rate dependent, there is an increased tendency for crack penetration. Due to the local and instantaneous rate dependence of strength and toughness, the previously established criteria in terms of the quasistatic property ratios are shown to be inapplicable. Alternatively, modeling is deemed inevitable for which the main source of uncertainty comes from the boundary conditions, which are shown to significantly affect the predicted cracking behavior.

Coupled viscosity-damage model for concrete under high strain rate

A coupled viscosity-damage model of concrete under high strain rate is proposed based on the bi-scalar plastic-damage model. A rheological model is provided to explain the time delay mechanism of the damage under dynamic loading. A rate-dependent damage evolution is established by introducing the Duvaut–Lions type of the damage driving stress rate, and damage and viscosity are coupled. The operator splitting method is used to design an explicit calculation procedure. It is illustrated how the damage evolution predicted by the model differs for dynamic loading and quasi-static loading. Excellent comparisons between the simulated and experimental results show that the model can be used to reflect the strain rate effect of concrete under impact.

A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence

Carbon fiber reinforced thermoplastic polymer (CFRTP) laminates can be used in packaging electronics components to reduce weight and shield external disturbance. The CFRTP structures in operation are inevitably to suffer dynamic loading conditions such as falling rocks, tools and impacts. In this study, a strain rate dependent material model for accurately evaluating the dynamic response of CFRTP laminates with different stacking sequence was proposed. The model was composed of three components: a strain rate dependent constitute model, a strain rate related damage initiation model and an energy-based damage evolution model. The strain rate effect of modulus and strength was described by a stacking sequence related matrix, and the damage initiation model could describe the matrix, fiber and delamination damage of CFRTP laminates without introducing cohesive elements. The material model was implemented into finite element software ABAQUS by user defines subroutine VUMAT. The low velocity impact tests of CFRTP laminates with quasi-isotropic and angle-ply stacking sequence were used to provide validation data. The dynamic response of CFRTP laminates from numerical results were highly consistent with the experimental results. The mechanical response of CFRTP laminates were affected by stacking sequence and impact energy, and the numerical error of proposed material model significantly decreased with the increasing impact energy especially for the laminae with damage occur.

Impact simulation of composite panels for aerospace applications

The aerospace research community has been working towards the development of a comprehensive framework for the design of composite structures at the component, subassembly, assembly, and system levels. Such a framework requires accurate, efficient and easy-to-use mathematical and computational models that are in sync with physical reality. The research work in this paper is designed to help an aerospace structural engineer move towards this goal by simulating dynamic impact to composite panels. First, the existing orthotropic visco-elastic visco-plastic material model in LS-DYNA commercial finite element program, MAT_COMPOSITE_TABULATED_PLASTICITY_DAMAGE (MAT_213) is enhanced with the development and use of rate-dependent damage data. Using state-of-the-art experimental procedures, impact validation test data are created. Second, the versatility of the constitutive model is examined by its ability to simulate a low velocity (27 ft/s, 8 m/s) impact test, and two high velocity impact tests (385–417 ft/s, 117–127 m/s) that straddle the ballistic limit of the projectile and the composite panels. Third, these impact events are modeled using three different finite element types – under-integrated and fully-integrated solid elements, and fully-integrated thin shell elements. Insight into accuracy versus numerical efficiency is gained by comparing the performance of solid versus thin shell elements. The numerical results show that accurate predictions of these impact events can be obtained with reasonable effort and care.

A rate-dependent damage model to characterize dynamic fracture behavior of Ti6Al4V under high strain rate loading

Material damage and fracture behavior are affected by loading rates. This paper aims to investigate dynamic deformation and fracture mechanisms of Ti6Al4V over a wide strain rate range from quasi-static to 104 /s. A high strain rate test apparatus is developed and a new rate-dependent material damage law is proposed. The damage energy of Ti6Al4V keeps nearly constant at the strain rate lower than 10 /s, while it declines dramatically under the strain rate high than 103 /s. Ductile to brittle transition of Ti6Al4V occurs at the strain rate of 16,000 /s, which leads to the transition of material fracture mechanism from adiabatic shear to embrittlement fracture. The research proves that developing appropriate damage evolution law is important to improve prediction accuracy of material deformation and guarantee structural design safety especially for dynamic loading components.

A Nonlinear Viscoelastic Constitutive Model for Solid Propellant with Rate-Dependent Cumulative Damage.

Solid propellant is a composite material exhibiting classic nonlinear viscoelastic mechanical characteristic, which is due in a large part to a cumulative damage process caused by the formation and growth of microflaws inside. The standard relaxation tests and uniaxial tension tests under different velocities of hydroxyl-terminated polybutadiene (HTPB) propellant are carried out in this paper, where Digital Image Correlation (DIC) technique is applied to record deformation. The experimental results show that the material mechanical behavior is rate-dependent. It is also observed that the yield stress and failure stress are significantly rate-dependent on the tensile velocity. Based on these experimental results, it can be inferred that the stiffness degradation and damage evolution of HTPB propellant are a rate-dependent processes. Therefore, the damage accumulation of HTPB propellant is considered rate-dependent in this research. In order to describe the mechanical characteristic precisely, a nonlinear viscoelastic constitutive model with rate-dependent cumulative damage is developed. The damage model is developed based on the concept of pseudo strain, in which a Prony series representation of viscoelastic material functions is applied. Besides, a rate-dependent damage variable is introduced into the model through considering the rate-dependent characteristics of cumulative damage process. In addition, a new normalized failure criterion is derived on the basis of the proposed damage model, which is independent of strain-rate after normalization. Finally, it is implemented in commercial finite element software for stress analysis to verify the predictive capacities of the damage model. The accuracy of the constitutive model and failure criterion is validated under uniaxial tensile tests of various strain rates.

Dynamic tensile fracture of liquid copper containing helium bubbles

The dynamic tensile fracture process of liquid copper containing helium bubbles system is systematically investigated by molecular dynamics simulations and theoretical modeling. A strain rate-dependent damage mechanism that transforms from a co-growth of voids and helium bubbles to a sole expansion of helium bubbles as the strain rate decreases is firstly found, and a corresponding physical explanation is proposed. Meanwhile, it is found that the dynamic tensile strength of the material is significant affected by the transition of the damage mechanism. Based on the revealed damage mechanism and the basic properties of helium bubbles such as internal pressure and surface tension obtained with the help of molecular dynamics simulations, a mechanical model is constructed to describe the dynamic damage process of the system. The volume evolution of each helium bubble as well as stress evolution of the system obtained from molecular dynamics simulations is well reproduced by the mechanical model in a wide range of strain rate. The strain rate-dependent damage mechanism and the proposed theoretical damage model will provide insights into understanding the dynamic responses of metals containing initial bubbles under extreme conditions.