Energy-based Failure Criterion Research Articles

Objective determination of peridynamic material parameters for fiber-reinforced composites with shear nonlinearity – Part 2: Strength properties and strain rate dependence

Formulation and implementation of peridynamic strength parameters and strain rate-dependent behavior of fiber-reinforced composite laminates are presented. This work builds on the earlier framework [1] objectively determining elastic parameters for laminates exhibiting shear nonlinearity. The formulation of the strength parameters uses energy-based failure criteria, specifically addressing intralaminar and interlaminar behaviors. A novel implementation of strain rate effects includes conversion from local strain to nonlocal stretch rates. The current peridynamic approach with shear nonlinearity and strain rate dependence accurately captures multiple experimentally measured metrics, including force vs. time, force vs. displacement, energy vs. time, and damage and delamination extents.

A peridynamic model for electromechanical fracture and crack propagation in piezoelectric solids

This paper presents for the first time an approach to the problem of electromechanical fracture and crack propagation in piezoelectric solids with peridynamics. Fracture in piezoelectric ceramics is an important problem in engineering due to its complexity. The majority of the computational models available on the literature rely on sharp crack representations, which have difficulties dealing with complex crack patterns, or rely on diffusive crack models, such as the phase-field fracture model, that can predict complex patterns but does not represent cracks in a discrete way. On the other hand, peridynamics has been designed to solve this problems and is able to simulate discrete cracks as well as complex crack phenomena like fragmentation and branching. We present a novel approach to the implementation of different electric crack face boundary conditions in a peridynamic way, by a field selective bond breaking approach. Moreover, it is also presented the first electromechanical failure criterion for fracture in piezoelectric ceramics. We develop an energy based failure criterion due to its generality and wide range of applications. These approaches are presented in a way such that they are valid for any type of peridynamic formulation. The used numerical model is implemented using correspondence-based peridynamics with the linear piezoelectricity constitutive setting, using a meshfree discretization and solved quasi-statically with an implicit incremental-iterative scheme. Numerical examples are presented to demonstrate the capabilities of these new approaches and assess the performance of the model against experimental results. The model is capable of numerically predicting complicated fracture behaviour and crack propagation in an intrinsic/autonomous way, as demonstrated by the results.

A kinetic energy-based failure criterion for defining slope stability by PFEM strength reduction

From the perspective of energy, the change of kinetic energy is rather obvious in the process of slope from steady state to failure. To numerically define the factor of safety (FOS) of the slope, the strength reduction method (SRM) is coupled with the two-dimensional explicit smoothed particle finite element method (eSPFEM), considered kinetic energy, to analyze slope stability. Through the failure analysis of slope, a new failure criterion based on the change of occurrence time of peak kinetic energy is proposed in this paper. Its applicability and accuracy are verified by two homogeneous slopes and two inhomogeneous slopes. The results show that the evolution of kinetic energy in the slope can intuitively and effectively reveal the sudden change of occurrence time of peak kinetic energy, leading to objectively determining the FOS of the slope. The proposed failure criterion regarding the characteristics of kinetic energy evolution could be further utilized in practical engineering to determine a more accurate factor of safety of the slope.

A peridynamic differential operator-based scheme for the extended bond-based peridynamics and its application to fracture problems of brittle solids

In order to describe the mechanical behavior of solids with arbitrary Poisson’s ratio values, an extended bond-based peridynamic (XBB-PD) model was developed in the authors’ previous work by taking both the bond longitudinal and tangential deformations into account. In the current work, a peridynamic differential operator based implementation scheme is presented for the XBB-PD model. An energy-based failure criterion is introduced to describe the failure and crack propagation in brittle solids. First, two elastic examples are solved to validate the proposed approach. The m- and δ- convergence studies are carried out. Subsequentially, several numerical examples of crack propagation problems are simulated. All simulations show good agreement with the results reported in the references, demonstrating the flexibility and capabilities of the developed approach in the simulation of crack propagation in brittle solids.

An improved four-parameter conjugated bond-based peridynamic method for fiber-reinforced composites

The classical bond-based peridynamic (BB-PD) theory has inherent limitations on material properties when dealing with composites. An improved lamina conjugated BB-PD model with four independent material parameters is established to study the fracture behavior of composite materials. The model defines four basic generalized PD bonds, including fiber bond, matrix bond, fiber-matrix conjugated bond pair and matrix-matrix conjugated bond pair. Using the equivalent relationship of elastic strain energy density, the analytical expressions of the four micro-modulus in the improved lamina conjugated BB-PD model are determined. These four micro-modulus parameters can describe the four independent engineering material constants of the lamina, which eliminates the restriction of Poisson’s ratio and shear elastic modulus for the composite materials. Moreover, an energy-based failure criterion is further proposed for the failure analysis of composite materials. In order to verify the capability and applicability of the proposed model, the displacement field and fracture behavior of the composite lamina with uniaxial tensile are simulated. In addition, the failure modes and crack propagation path of the laminae with different fiber orientations and initial crack angles are investigated by using the proposed model.

Investigating the effect of notch size on critical distance and fatigue limit by coupling the theory of critical distance and finite fracture mechanics

The energy based failure criterion Finite Fracture Mechanics is transformed into a stress based failure criterion and expressed by an effective stress similar with Line Method. After coupling the two criterions, the theoretical critical distance expression is derived based on notch stress distribution, stress intensity factor function and material characteristic length. The effect of notch size and material characteristic length on the critical distance and fatigue limit prediction was analyzed for a group of V-shaped notches. Then, the coupled method was validated by a large number of experimental results. It is revealed that the Line Method and coupled method are the same except that they employ different critical distances. The validity of Line Method was discussed based on the difference of critical distances and fatigue limit predictions between the Line Method and coupled method.

Mode-Independent and Mode-Interactive Failure Criteria for Unidirectional Composites Based on Strain Energy Density.

The strain energy released plays a crucial role in generating macroscopic failure in unidirectional (UD) composites. This paper proposes two new strain energy-based failure criteria, regarding fiber-dominated and matrix-dominated failure mode as independent and interactive, respectively. The failure expression is formulated based on rigorous mathematical deducing, accompanied by physical interpretation. Based on the lack of experimentally feasible multi-axial strengths, a predefined assumption of infinite strength under bi-axial and tri-axial compressive stress provides the possibility for determining all coefficients only by using conventional uniaxial strengths. The failure envelopes predicted by the proposed criteria have been validated against experimental results under biaxial, off-axis and tri-axial loading cases. A better agreement with physical reality was achieved by the failure mode-interactive criterion, suggesting a wide range of applicability.

A generalized bond-based peridynamic model for quasi-brittle materials enriched with bond tension–rotation–shear coupling effects

A generalized bond-based micropolar peridynamic model is proposed to simulate the nonlinear deformation and mixed-mode crack propagation of quasi-brittle materials under arbitrary dynamic loads. The mechanical behaviors of the material points are reformulated by incorporating the bond tension–rotation–shear coupling effects, which makes the model suitable for complex discontinuous problems in both three-dimensional spatial and two-dimensional plane conditions. The governing equations of the bond are established by employing the Timoshenko beam theory to simulate the interaction between material points as well as the bond coupling effect. Three kinds of peridynamic parameters, corresponding to the compressive, shear and bending stiffness of the bond, are introduced to keep the consistence of the strain energy obtained from the proposed peridynamic model and from the continuum mechanics under arbitrary deformation fields. Moreover, a novel energy-based failure criterion, involving the maximum stretch, shear strain and rotation angle limits of the bond, is proposed to describe the nonlinear behaviors and progressive failure for general quasi-brittle materials. The proposed model is verified by providing comparisons between its results and those from known analytical solutions and experimental observations. The influences of the bond tension–rotation–shear coupling effect as well as the applicability of the proposed model for the wave propagation, complex deformation and mix-mode fracture problems are also investigated. Results show that the proposed model with the bond coupling effect will greatly improve the simulation accuracy for dynamic problems of quasi-brittle materials under complex loading conditions. Results also indicate that the proposed model can well capture the nonlinear deformation, crack propagation, as well as progressive failure of materials with variable Poisson’s ratios under complex combined loads

Matrix cracking initiation, propagation and laminate failure in multiple plies of general symmetric composite laminates

This paper formulates an analytical model based on intrinsic material properties to predict ply cracking initiation and propagation in multiple plies and its impact on laminate strength in general symmetric laminates (possibly made of thin-plies) under combined triaxial normal loads and in-plane and out-of-plane shear loads while the effect of thermal residual stresses and statistical distribution of fracture energies are considered. To do so, a novel complete homogenization technique combined with recently developed accurate stress transfer models is implemented in conjunction with multi-axial energy-based failure criteria, Monte Carlo type of simulation and a strain-based fiber failure criterion. The model predictions show very good agreement with experimental results.

Failure of Porous Metals Based on Strain Energy Density Criterion

Abstract Porosity in metals is well known to influence the mechanical behavior, namely, the elastic response, the plastic behavior, and the material loading capacity. The main focus of the current work is to investigate the failure of porous metals. Extensive literature search was conducted to identify failure mechanisms associated with the increase of porosity for up to 15% by volume. Consequently, micromechanical modeling is utilized to investigate the damage process at microlengths. Finally, a complete macromechanical modeling approach is proposed for specimen-sized models. The approach utilizes the extended Ramberg–Osgood relationship for the elastoplastic behavior, while the failure is predicted using a strain energy-based failure criterion capturing the effect of porosity. The proposed approach is validated against several testing results for different metals at various porosity levels.

Micromechanical progressive damage analysis of inter- and intra-layer failures in fiber-reinforced composite laminates

We analyze progressive damage and failure of composite laminates by using a micromechanical bridging model and compare numerical and experimental results for three fracture problems, namely, the four-point bending, the simple tension, and the simple tension of a laminate with an open hole at its centroid. These problems involve fiber–matrix interface debonding, constituents’ damage, interlayer delamination, and localized damage due to stress concentration. Macroscopic constitutive equations of unidirectional lamina, derived from those of the fiber and the matrix by using the bridging model with the fiber material assumed to be linearly elastic and the matrix to be elasto-plastic obeying the Drucker–Prager yield criterion, are employed. Strains in each constituent of the composite are assumed to be infinitesimal for the additive decomposition of strains into elastic and plastic parts to be valid, and the incremental plasticity theory is used. Stresses in the two constituents are found from their values in the homogenized material by using a dehomogenization technique. The intra-layer damage is assumed to initiate at a material point when the failure criterion for either the fiber or the matrix is satisfied. Young’s modulus of a constituent is degraded by following a Weibull distribution. A finite element is deleted when an energy-based failure criterion is satisfied in it, and the analysis is continued till the structure fails. The delamination between adjacent plies is simulated by including a thin resin layer at the interface and studying failure initiation and propagation in it. The computed reaction force versus the displacement curves and the failure patterns in the three problems are found to agree with the corresponding experimental data.

A dissipated pseudo strain energy-based failure criterion for thermal cracking and its verification using thermal stress restrained specimen tests

Low-temperature cracking is one of the most prevalent types of distress in asphalt concrete pavements in regions where the air temperature undergoes a significant daily drop. This paper proposes a failure criterion that correlates the dissipated pseudo strain energy (DPSE) at the time of failure with the reduced strain rate. Uniaxial direct tension monotonic tests, axial compression dynamic modulus tests, and direct tension cyclic fatigue tests were performed using the Asphalt Mixture Performance Tester (AMPT) for a wide range of asphalt mixtures with different reclaimed asphalt pavement (RAP) contents, binder contents, virgin binder performance grades, and aging levels. The results show that the simplified viscoelastic continuum damage (S-VECD) model, which is characterized by the dynamic modulus and cyclic fatigue test results, can predict the stress-strain behavior of a given mixture subjected to monotonic tests at different temperatures and loading rates. This finding allows the prediction of DPSE in monotonic tension tests using the S-VECD model. The thermal stress restrained specimen test (TSRST) was then used to verify the DPSE-based failure criterion and the ability of the S-VECD model to predict thermal fracture behavior. The study results show that the predicted fracture temperatures match the measured ones for the study mixtures with reasonable accuracy. The study also used data from mixtures whose RAP contents, binder contents, virgin binder grades, and aging levels were systematically altered to verify the reasonableness of the proposed procedure to evaluate the differences in thermal fracture performance that are due to changes in these factors. The ability to predict the fracture stress and fracture temperature measured via the TSRST using the S-VECD model and the suggested DPSE failure criterion is of substantial practical and technical importance because it allows the prediction of both fatigue cracking and thermal cracking using a single set of tests, i.e., AMPT dynamic modulus and cyclic fatigue tests.

A failure criterion to predict the onset of matrix cracking induced delamination in general composite laminates

In this study, a new energy-based failure criterion is developed to predict the onset and growth of matrix cracking induced delamination, known as MCID in composite laminates. This criterion is formulated upon the concept of fracture mechanics by comparison of energy release rate obtained due to MCID and interface fracture toughness. This failure criterion is developed as a general model so that it can be appropriated for any arbitrary lay-up, under any in-plane or out of plane loading. The developed failure criterion is validated against several experimental studies in the unconstraint condition. It is revealed that the criterion is of excellent agreement with the experimental results. Furthermore, for the generalized plane strain condition, validation is performed using two different models. Lastly, some of the potential applications of the proposed failure criterion are presented in different laminates. Considering the unique characteristics of this criterion, it can be employed along with other failure criteria in the design of composite structures.

Peridynamic Modeling of Mode-I Delamination Growth in Double Cantilever Composite Beam Test: A Two-Dimensional Modeling Using Revised Energy-Based Failure Criteria

This study presents a two-dimensional ordinary state-based peridynamic (OSB PD) modeling of mode-I delamination growth in a double cantilever composite beam (DCB) test using revised energy-based failure criteria. The two-dimensional OSB PD composite model for DCB modeling is obtained by reformulating the previous OSB PD lamina model in x–z direction. The revised energy-based failure criteria are derived following the approach of establishing the relationship between critical bond breakage work and energy release rate. Loading increment convergence analysis and grid spacing influence study are conducted to investigate the reliability of the present modeling. The peridynamic (PD) modeling load–displacement curve and delamination growth process are then quantitatively compared with experimental results obtained from standard tests of composite DCB samples, which show good agreement between the modeling results and experimental results. The PD modeling delamination growth process damage contours are also illustrated. Finally, the influence of the revised energy-based failure criteria is investigated. The results show that the revised energy-based failure criteria improve the accuracy of the PD delamination modeling of DCB test significantly.

Peridynamic Open-Hole Tensile Strength Prediction of Fiber-Reinforced Composite Laminate Using Energy-Based Failure Criteria

In the present study, peridynamic (PD) open-hole tensile (OHT) strength prediction of fiber-reinforced composite laminate using energy-based failure criteria is conducted. Spherical-horizon peridynamic laminate theory (PDLT) model is used. Energy-based failure criteria are introduced into the model. Delamination fracture modes can be distinguished in the present energy-based failure criteria. Three OHT testing results of fiber-reinforced composite laminate are chosen from literatures and used as benchmarks to validate the present PD composite model with energy-based failure criteria. It is shown that the PD predicted OHT strength fits the experimental results quite well. From the predicted displacement field, the fracture surface can be clearly detected. Typical damage modes of composite, fiber breakage, matrix crack, and delamination, are also illustrated in detail for each specimen. Numerical results in the present study validate the accuracy and reliability of the present PD composite model with energy-based failure criteria.

Physical stochastic damage model for concrete subjected to fatigue loading

A unified damage model applicable to both monotonic and fatigue loading is developed for concrete in the framework of mesoscopic stochastic fracture models. Besides traditional strain-based failure criteria, a new kind of energy-based failure criteria for meso-elements is established relying on nanoscale mechanics. Verifications show that the proposed model can not only reasonably reproduce the randomness in fatigue lifetime but also well describe the nonlinearity in fatigue damage evolution of concrete. In addition, the physical mechanisms lying behind these randomness and nonlinearity are clearly demonstrated for the first time.

Peridynamic analysis of fibre-matrix debond and matrix failure mechanisms in composites under transverse tensile load by an energy-based damage criterion

Reliable simulation methods and failure criteria are required during the sizing of fibre reinforced plastics (FRPs). Peridynamics (PDs) is a promising numerical method to predict the evolution and interaction of damages. In the current text a novel energy-based failure criterion for linear peridynamic solid (LPS) materials is implemented and applied to the micromechanical damage of FRP structures. The novel criterion promises a more realistic reproduction of failure modes for ductile materials, a reduced mesh dependency and only requires physically measurable parameters. The results of the novel criterion are compared to a reference criterion and are evaluated against experimental observations.

Development of a pseudo strain energy-based fatigue failure criterion for asphalt mixtures

This paper presents a new energy-based failure criterion that is based on the simplified viscoelastic continuum damage model. This study found that the average reduction in pseudo stiffness up to failure, referred to here as DR, is a material constant that is independent of mode of loading, temperature, and stress/strain amplitude. Twenty different asphalt mixtures were used to validate the proposed method. This paper presents typical values of DR and shows that the DR changes with the mixture characteristics. The advantages of the DR failure criterion over a previous failure criterion (known as the GR criterion) are that it: (1) allows the prediction of fatigue failure in arithmetic scale, which reduces possible errors due to extrapolation of the accelerated laboratory fatigue test data to realistic traffic volumes encountered in the field and (2) reduces the number of tests required to characterise the failure criterion. Statistical analysis was performed in this study and the results show confidence levels that can be obtained from two or three fatigue tests.

Numerical study on the structural response of blast-loaded thin aluminium and steel plates

The inelastic response of thin aluminium and steel plates subjected to airblast loading is studied numerically and validated against experimental data. Special focus is placed on the influence of elastic effects and negative phase on the structural response. The blast loading was varied by detonating spherical charges of plastic explosives at various stand-off distances relative to the centre point of the plates. The numerical results obtained with the finite element code EUROPLEXUS were in good agreement with the experiments and predicted the entire range of structural response from complete tearing at the supports to a more counter-intuitive behaviour (CIB) where the final configuration of the plate was in the opposite direction to the incident blast wave due to reversed snap buckling (RSB). RSB attracted special attention since this is an unstable configuration sensitive to small changes in the loading and in structural characteristics. The negative phase of the blast pressure is usually neglected in blast-resistant design. However, the numerical simulations showed that the negative overpressure dominated the structural response and led to RSB at some loading and structural conditions. Two distinctive types of CIB were identified and both were found to depend on the timing and magnitude of the peak negative overpressure relative to the dynamic response of the plates. The study also revealed that CIB may occur in thin plates when the negative impulse is of the same order of magnitude as the positive impulse. The partial and complete failure along the boundaries observed in some of the tests was also successfully recreated in the simulations by using an energy-based failure criterion and element erosion.

Application of Time-Temperature Superposition Principle on Fatigue Failure Analysis of Asphalt Binder

The linear amplitude sweep (LAS) test has been proposed for fatigue specifications of asphalt binders. Recently, a newly developed fatigue failure definition and energy-based failure criterion have been proposed for improving the LAS procedure and data interpreting; however, these improvements only affect LAS data conducted at a constant temperature. This paper, therefore, discusses the loading temperature effects on LAS-based binder fatigue, damage evolution, and final fatigue failure occurrence. Experimental results indicate that both damage characteristic curves (DCCs) and the failure criterion derived from the simplified-viscoelastic continuum damage (S-VECD) model are strongly affected by the testing temperature. However, the temperature shift factors determined from the dynamic shear modulus testing within the linear viscoelastic domain have been proven to be effective in eliminating the temperature influence for both fatigue DCCs and the failure criterion. The validation on binder phase demonstrates that the time-temperature superposition principle (TTSP) shift factor is only a function of temperature and is independent of strain level. TTSP application on both undamaged and damaged material behaviors is able to greatly improve the testing efficiency of the LAS-based binder fatigue characterization.