Phenomenological Failure Criteria Research Articles

On the Importance of Including Cohesive Zone Models in Modelling Mixed-Mode Aneurysm Rupture.

The precise mechanism of rupture in abdominal aortic aneurysms (AAAs) has not yet been uncovered. The phenomenological failure criterion of the coefficient of proportionality between von Mises stress and tissue strength does not account for any mechanistic foundation of tissue fracture. Experimental studies have shown that arterial failure is a stepwise process of fibrous delamination (mode II) and kinking (mode I) between layers. Such a mechanism has not previously been considered for AAA rupture. In the current study we consider both von Mises stress in the wall, in addition to interlayer tractions and delamination using cohesive zone models. Firstly, we present a parametric investigation of the influence of a range of AAA anatomical features on the likelihood of elevated interlayer traction and delamination. We observe in several cases that the location of peak von Mises stress and tangential traction coincide. Our simulations also reveal however, that peak von Mises and intramural tractions are not coincident for aneurysms with Length/Radius less than 2 (short high-curvature aneurysms) and for aneurysms with symmetric intraluminal thrombus (ILT). For an aneurysm with (L/R = 2.0), the peak moves slightly towards the origin while the peak is near the peak bulge with a separation distance of ~ 17mm. Additionally, we present three patient-specific AAA models derived directly from CT scans, which also illustrate that the location of von Mises stress does not correlate with the point of interlayer delamination. This study suggests that incorporating cohesive zone models into clinical based FE analyses may capture a greater proportion of ruptures in-silico.

Phenomenological failure criteria analysis of a composite bolted joint under multi-axial loading using the finite element method

Carbon Fiber Reinforced Polymer Composites (CFRP) are commonly used in various sectors due to their excellent properties. However, they present complex failure modes, particularly in bolted joints, which are widely used in the aeronautical industry due to their ease of assembly and disassembly. Phenomenological failure criteria can be used to evaluate failure modes analytically and reduce the number of experimental tests. It is important to determine the criterion that best reflects reality. The Hashin, Puck, and LaRC04 failure criteria were evaluated using a finite element method software - FEMAP 2021.2 educational version - through simulation. Numerical simulations were conducted on a 2D model of a carbon/epoxy composite bolted joint under multiaxial loads, following ASTM D5661 dimensions. The failure criteria were compared to determine the most appropriate one for this type of component. Among the evaluated criteria, the Hashin criterion showed an intermediate level, while the Puck criterion was the most conservative and the LaRC04 criterion was the least conservative. It is recommended to use the Hashin criterion for general analyses. For analyses that require a detailed examination of compression failure modes, it is recommended to use the LaRC04 criterion. The Puck criterion is suggested for more conservative analyses.

A bond-level energy-based peridynamics for mixed-mode fracture in rocks

This paper deals with the numerical simulation of initiation and propagation of mixed mode fracture in rocks. A bond-level energy-based peridynamic model is developed by introducing a dilatation function to capture both volumetric and deviatoric deformations. We proceed to define the nonlocal stresses to obtain the isotropic and deviatoric forces commensurate with the deformations. We then come up with a new failure model to link computational peridynamics with some phenomenological failure criteria, which is highly relevant for both brittle and quasi-brittle rocks. Finally, several numerical examples of mixed-mode fractures are presented to show the performance of our model.

Phase field fracture in elasto-plastic solids: Incorporating phenomenological failure criteria for ductile materials

Phase field approaches have been developed to analyze the failure behavior of ductile materials. In the previous phase field models, a constant critical energy or strain threshold is commonly introduced to the formulation of the driving force, aiming to avoid damage initiation at a low level of elastic and plastic deformations. However, it may not suffice to describe complex ductile fracture behavior of materials subject to various stress states. In this study, a new phase field approach is proposed to consider the effects of stress triaxiality and Lode angle, by incorporating phenomenological ductile fracture criteria. The proposed models are formulated using variational principles and implemented numerically in the finite element framework. Analytical homogeneous solutions for uniaxial tension, simple shear, and equibiaxial tension loads are derived to demonstrate the effectiveness of the proposed models. Three groups of numerical examples, covering a wide range of stress states, are utilized to further examine the proposed models. The results show that the models can reproduce the experimental response of the specimen in terms of force versus displacement curve, crack initiation, and crack propagation under various loading conditions. The proposed models are able to capture the stress-state dependence of fracture behavior of ductile materials.

An extended invariant approach to laminate failure of fibre-reinforced polymer structures

AbstractThis paper presents the extension and validation of omni-failure envelopes for first-ply failure (FPF) and last-ply failure (LPF) analysis of advanced composite materials under general three-dimensional (3D) stress states. Phenomenological failure criteria based on invariant structural tensors are implemented to address failure events in multidirectional laminates using the “omni strain failure envelope” concept. This concept enables the generation of safe predictions of FPF and LPF of composite laminates, providing reliable and fast laminate failure indications that can be particularly useful as a design tool for conceptual and preliminary design of composite structures. The proposed extended omni strain failure envelopes allow not only identification of the controlling plies for FPF and LPF, but also of the controlling failure modes. FPF/LPF surfaces for general 3D stress states can be obtained using only the material properties extracted from the unidirectional (UD) material, and can predict membrane FPF or LPF of any laminate independently of lay-up, while considering the effect of out-of-plane stresses. The predictions of the LPF envelopes and surfaces are compared with experimental data on multidirectional laminates from the first and second World-Wide Failure Exercise (WWFE), showing a satisfactory agreement and validating the conservative character of omni-failure envelopes also in the presence of high levels of triaxiality.

Distortional‐dilatational strain failure mode concept for hyperelastic materials

This work presents a universal, generally applicable, phenomenological failure criterion that describes a single, smooth, and convex hypersurface in principal strain space. It provides a strain‐based description of the bulk material failure of nearly incompressible hyperelastic elastomers and captures both distortional and volumetric failure in a single criterion.

An Extension Strain Type Mohr\u2013Coulomb Criterion

Extension fractures are typical for the deformation under low or no confining pressure. They can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. In this article, it is shown that the simple extension strain criterion makes unrealistic strength predictions in biaxial compression and tension. To overcome this major limitation, a new extension strain criterion is proposed by adding a weighted principal shear component to the simple criterion. The shear weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting extension failure modes, which are unexpected in the classical understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain leading to dilatancy. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak stress CP. Different from compressive loading, tensile loading requires only a limited number of critical cracks to cause failure. Therefore, for tensile stresses, the failure criteria must be modified somehow, possibly by a cut-off corresponding to the CI stress. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.

Modelling of ductile fracture in ship structures subjected to quasi-static impact loads

A phenomenological failure criterion, which attempts to achieve a tradeoff between simplicity and prediction quality, is developed to predict the fracture behavior of ship structures under quasi-static impact loads. For simplicity, only the dominant physical mechanism remains in the model. In high stress triaxiality regime, it is believed that ductile fracture is mainly influenced by the stress triaxiality, while under low stress triaxiality regime, Lode angle is considered as the key factor in the fracture prediction. Thus, the combined maximum shear stress and Rice Tracey (MSSRT) criterion is developed to cover a wide range of stress states. The calibration parameters in the criterion can be determined from the uniaxial tensile test only, which is suitable for industrial application where available material data are limited.Along with the fracture scaling framework, the developed failure criterion is implemented into the explicit finite element code LS-DYNA, and the performance of the failure criterion is evaluated by making comparisons with a series of indentation tests involving different materials, structural arrangements and indenter sizes. It is shown that the fracture behavior is well predicted by simulations for all cases. Besides, comparisons among different failure criteria are also carried out. It is found that MSSRT criterion could generate more consistent results when compared with other commonly used failure criteria.

Towards an enhanced fatigue evaluation of bituminous mortars

The fatigue resistance, as a performance indicator, is of paramount importance for the selection and benchmarking of bituminous materials. The bituminous mortar can be considered as the medium that connects and envelopes the coarse aggregate skeleton, and hence will significantly influence the fatigue resistance at bulk-scale. Therefore this study presents the steps and challenges of a new testing framework to evaluate the fatigue resistance of bituminous mortars. To do so, first, a new test geometry is introduced, which will ensure cohesive failure in a predefined area. The integrity of this sample geometry is assessed theoretically through finite element simulations and by computer tomography scans. Secondly, specimens of the new geometry are evaluated experimentally using a dynamic shear rheometer, where time-sweep tests are performed on two control mortar types under various test conditions. The control mortar types are fabricated using two commercial bituminous binders, one modified and one neat binder, to evaluate the effect of binder type. The test results are comprehensively analysed using fundamental dissipated energy-based concepts but also empirical and phenomenological failure criteria, providing insights into the failure evolution. For the tested mortar types, the analysis shows good convergence with the considered fatigue models. Finally, using dissipated energy concepts led to the most consisted fatigue model, which is independent of binder type and test conditions.

Experimental assessment of failure criteria for the interaction of normal stress perpendicular to the grain with rolling shear stress in Norway spruce clear wood

The anisotropic material behavior of wood, considered as a cylindrically orthotropic material with annual rings, leads to several different failure mechanisms already under uniaxial stresses. Stress interaction becomes important in the engineering design of structural elements and is often predicted by failure criteria based on uniaxial properties. The prediction quality of failure criteria has been assessed with longitudinal shear stress interaction, though less is known on rolling shear stress in interaction with stress perpendicular to the grain. The study aims at investigating the corresponding mechanical behavior of Norway spruce (Picea abies) clear wood by validating failure envelopes for stress combinations in the cross-sectional plane, based on experimental investigations. For this purpose, a test setup that controls the stress interaction and loading of clear wood along pre-defined displacement paths needed to be developed. Experimentally defined failure states could then be compared to failure surfaces predicted by the phenomenological failure criteria. Material behavior was quantified in terms of stiffness, strength, and elastic and post-elastic responses on dog-bone shaped specimens loaded along 12 different displacement paths. A comparison with failure criteria for two nominal compressive strain levels showed that a combination of failure criteria would be required to represent the material behavior and consider the positive effect of compressive stresses on the rolling shear strength. The findings of this work will contribute to studying local stress distribution of structural elements and construction details, where stress interactions with rolling shear develop.

Computational micromechanics-based prediction of the failure of unidirectional composite lamina subjected to transverse and in-plane shear stress states

This paper presents a micromechanics-based 3D finite element model for predicting the damage initiation, propagation, and failure strength of TC33/Epoxy carbon fiber reinforced polymer (CFRP) unidirectional lamina under biaxial loadings. The finite element model is generated by introducing representative volume element (RVE) with a random distribution of fibers and a non-zero thickness, numerically identified interface phase via cohesive elements. In the finite element model, the carbon fibers are considered as elastic, while the elasto-plastic behavior and damage of the matrix are governed by extended Drucker–Prager plastic yielding model and ductile damage criterion. By imposing periodic boundary conditions to the RVEs, various cases subjected to uniaxial and biaxial loading conditions are carried out. During the combined transverse and in-plane shear stress states, a failure transition from compression- or tension-dominated to shear-dominated is captured, and the effects of the interfacial strength on the transition damage mechanisms are discussed. The corresponding failure locus is compared with the upper bound and lower bound predictions of three phenomenological failure criteria (Hashin, Tasi–Wu, and Puck failure criteria) for composites. It was found that in the interface-dominated failure of a CFRP lamina with a weak interface, the Hashin failure criterion performs best among the currently popular failure criteria. However, in the matrix-dominated failure with a strong interface, the Puck failure criterion performs best. Comparing these three criteria, it can be seen the Tsai–Wu may be generally better than both of others as it presents more neutral predictions in both of the examined cases.

Progressive failure of composite wind blades with a shear-web spar subjected to static testing

Composite wind blades of 1m long comprising glass-fabric/epoxy skins and a sandwich plate-type spar were designed and fabricated for static testing. In the composite wind blades, the spar supports the top and bottom skins to form the airfoil shape of NACA4418. The blades were tested to failure and the failure modes were identified at different loading stages. A structural failure analysis method which consists of a geometrically nonlinear finite element (FE) model and appropriate phenomenological failure criteria is used to study the progressive failure behaviours of the blades subjected to different types of quasi-static loads. The experimental load-displacement curves as well as failure loads and locations for different failure modes are used to validate the suitability of the proposed failure analysis method.

Mechanical characterization and modeling of the deformation and failure of the highly crosslinked RTM6 epoxy resin

The nonlinear deformation and fracture of RTM6 epoxy resin is characterized as a function of strain rate and temperature under various loading conditions involving uniaxial tension, notched tension, uniaxial compression, torsion, and shear. The parameters of the hardening law depend on the strain-rate and temperature. The pressure-dependency and hardening law, as well as four different phenomenological failure criteria, are identified using a subset of the experimental results. Detailed fractography analysis provides insight into the competition between shear yielding and maximum principal stress driven brittle failure. The constitutive model and a stress-triaxiality dependent effective plastic strain based failure criterion are readily introduced in the standard version of Abaqus, without the need for coding user subroutines, and can thus be directly used as an input in multi-scale modeling of fibre-reinforced composite material. The model is successfully validated against data not used for the identification and through the full simulation of the crack propagation process in the V-notched beam shear test.

Quasi-static buckling and first-ply failure loads of shear web reinforced glass-fabric composite wind blades

A procedure is proposed to analyze the structural failure of a composite wind blade subjected to quasi-static loads. The structural failure of a wind blade under extreme wind loads which can be treated as quasi-static loads is an important issue to be tackled when assessing the reliability of a wind turbine. In the proposed structural failure analysis procedure, the geometrically nonlinear finite element (FE) method together with several phenomenological failure criteria is used to investigate the possible failure modes such as incipient buckling, interfacial debonding, and first-ply failure of the blade via an incremental loading approach. The failure loads and locations associated with the possible failure modes for a number of small wind blades with different structural configurations are determined to study the appropriateness of the failure criteria. Static tests of several small glass-fabric composite wind blades were conducted to validate the suitability of the proposed procedure. It has been shown that the experimentally and theoretically predicted failure processes of the wind blades are in good agreement. The applications of the proposed procedure are demonstrated by means of a numerical example in which the failure process of a wind blade under quasi-static wind loads is simulated.

Scale effect of explosive destruction of spherical vessels: Dynamic crack propagation and branching

• Proposed a damage model considering the material imperfection and rate dependent failure criterion, to account for explosively destruction. • FSI (Fluid Structure Interaction) simulation indicated that the elastic-plastic response of structure subjected to explosive loading has no scale effect when the damage model is not considered. However numerical crack analysis clearly shows the proposed damage model can well explain the cause of fracture and fragments of structures, as well as the transient crack propagation and branching process. • Provides a method to assessment the permissible load and corresponding extent of damage of explosively loaded structure, also the scale law was quantitatively acquired. Scale effect was repeatedly founded in Explosion containment vessels (ECVs) that with an increment of scale factor, the relative weight (the ratio of explosive destruction charge to the weight of vessel) decreased drastically. Also a reduction of the amount of deformation before failure and an increase in the tendency to the brittle failure were observed in large size structures. Though the scale effect was believed relevant with crack propagation energy and is decisive to the ultimate strength of explosively loaded structures, there's still no satisfying mechanism had been obtained in the past decades. In this paper, a numerical method combining with a phenomenological failure criterion was presented to re-examine the scale effect problems, where a failure criterion fully considering strain rate softening was implanted into the finite element code to account for the explosive destruction of the vessel. FSI (Fluid Structure Interaction) simulation and crack analysis covering the different scale factor from 1 to 10 were conducted, and the dynamical crack propagation and branching process was clearly revealed, which illuminates the cause of fracture and fragments of vessels, as well as the scale law of destruction charge. It was concluded that strain rate softening becomes more significant with an increase of strain rate, which leads to a rapid destruction in a very narrow region even the plastic deformation is too late to occur in the rest parts of the material, thus the brittle fracture mode was presented. The approach illustrated in this paper also provides an effective way to assessment the limit load of ECVs, which is helpful to prevent catastrophic brittle and quasi-brittle failure of the vessels.

Damage mechanics based design methodology for tidal current turbine composite blades

A material model based on the Puck phenomenological failure criteria for fibre and inter-fibre failure of glass-fibre and carbon-fibre reinforced polymer composites is presented. The model is applied through a user-defined material subroutine for 3D shell elements. Sub-modelling is used for detailed analysis of the highest stressed regions in the blades. The material model is incorporated into a methodology for the design and analysis of composite tidal current turbine blades. The methodology employs an iterative design process with respect to a number of failure criteria to ensure optimal structural and material performance of the blade. The methodology is automated using the Python programming language to enable efficient variation of model parameters for various design conditions. The forces acting on the blades are determined from blade element momentum theory for a number of turbine operating conditions. The results of a design case study for a typical horizontal axis device are presented to demonstrate the methodology.

On strain partitioning and micro-damage behavior of dual-phase steels

This work presents a model used to study strain partitioning and micro-damage initiation of various dual-phase steel microstructures. The model is formulated via continuum micro-mechanics and is solved in a finite-element framework. A phenomenological failure criterion is employed, calibrated and used to identify micro-damage initiation during plastic deformation.What is shown is how the primary microstructural parameters responsible for microstructural stress/strain fluctuations, namely phase strength contrast and hard phase fraction, influence phase averaged strains and phase specific strain distributions. Results of a study on micro-damage initiation show the influence of these primary microstructural parameters on strain for micro-damage initiation, the associated macro stress, and strain hardening.It is concluded that with rising microstructural mechanical heterogeneity, strain for micro-damage initiation decreases and strain hardening increases. Macroscopic stress at micro-damage initiation is shown to be primarily governed by the hard phase fraction and secondarily by the phase strength contrast.

Uniaxial and biaxial failure behaviors of aluminum alloy foams

Combined shear–tensile test have been performed on a closed-cell aluminum alloy foams with three relative densities over a wide range of loading rates in order to probe their failure behaviors under biaxial loading conditions. Quasi-static uniaxial compressive and tensile tests have also been conducted to investigate uniaxial failure behaviors of the aluminum alloy foams. The materials exhibit uniaxial failure stress asymmetry due to different failure mechanism in the uniaxial tensile and compression. Comparison is made between three phenomenological failure criteria and the measured failure stresses under different loading conditions to verify these criteria. The experimental failure surfaces of the aluminum alloy foams provide support for the three phenomenological failure criteria when suitable Poisson’s ratio is employed. The shape of the experimental failure surface in principal stress plane was not significantly influenced by variation in the relative density. The slight expansion of the failure surfaces with loading rate happened to be isotropic for this investigated closed-cell aluminum alloy foams in combined shear–tensile testes.

A three-dimensional wood material model to simulate the behavior of wood with any type of knot at the macro-scale

This article presents a three-dimensional wood material model implemented in finite element (FE) software which is capable of predicting the behavior of timber at the macro-scale taking into account the effect of any type of knot. The model was built in Ansys using the ansys parametric design language, such that the whole simulation process, including the creation of geometries, grain deviation, meshing and failure prediction, is automatically calculated by only introducing conventional measuring parameters of knots and locations of the pith. Knots are generated as elliptical, rotated and oblique cones. The local and global grain deviation is estimated by solving a multiphysics problem and equating the fibers of wood to the trajectory of laminar streamlines in 3-D. Wood is considered a transversely isotropic material with anisotropic plasticity in which the failure prediction is given by means of several phenomenological failure criteria. The model was validated with 4-point bending tests of Scots pine specimens showing errors in failure prediction of 5 %, errors in initial fracture location of less than 20 mm and errors of 9 % in photogrammetrically measured displacements of an average of 65 FE nodes, in which the heterogeneity of wood caused variations of up to 6 %.

Assessment of phenomenological failure criteria for wood

Many different phenomenological failure criteria have been proposed. These type of criteria do not explain the mechanism of failure itself. They merely identify failure (yes or no) and are usually regarded in practice as a simple and reliable tool for design. Most of them were developed for composite materials, but are extensively applied for wood. In this study, existing phenomenological strength criteria for orthotropic materials were applied to clear wood data. Instead of fitting the criteria to available experimental data, the criteria were used to predict failure of biaxial tests based on uniaxial strength. This procedure is closer to practice, and hence an answer to the question “is there any reliable failure criterion for wood?” Predictability of the criteria was assessed using normalisation procedure, and statistical significance of the difference of the means analysed. Based on the results, it can be concluded that a general criterion cannot be applied to predict failure, but should be chosen according to the biaxial stress state.