General Failure Criterion Research Articles

A failure criterion for genuinely orthotropic materials and integration of a series of criteria for materials of different degrees of anisotropy.

Existing failure criteria for orthotropic materials are subject to an underlying assumption which cause contradictions when applied to genuinely orthotropic materials that are significantly anisotropic in elasticity as well as in strengths. For such materials, there is lack of consistent failure criteria to support their applications in engineering structures. A general quadratic failure criterion tends to leave undetermined coefficients for interactive terms. A rational approach is adopted in this paper based on mathematical and logical considerations to determine these coefficients as the objective of this paper. Considerations are based on the intrinsic characteristics of the quadric surfaces introduced by the quadratic failure criterion. These coefficients must take the values as obtained, leaving no alternatives if logic prevails. The obtained criterion integrates for the first time a range of criteria separately formulated for materials of different degrees of anisotropy, from genuinely orthotropic, through transversely isotropic, cubically symmetric, to completely isotropic ones with different or identical tensile and compression strengths.

Shear Strength of Strain-Hardening Cementitious Materials

Concrete and other semi-brittle materials are pressure sensitive. Their resistance to shear depends on the confining pressure acting normal to the shear plane. This behaviour is modelled using experimentally calibrated failure criteria, such as the Mohr–Coulomb failure surface. Pressure sensitivity is also strongly evident in fibre-reinforced, strain-hardening cementitious composites (SHCC), despite the internal confinement these materials possess on account of their fibre content. However, because of the great range and variety of mixes used in such materials, no general failure criteria have yet been proposed. In this paper, the pressure-sensitive shear strength of SHCC containing short discontinuous PVA fibres is modelled with a three-parameter failure criterion. The parameters of the criterion are calibrated to the experimental results obtained from several tests that combine shear and normal pressure. These include uniaxial tension and compression, split tests, triaxial compression, and a series of push-off tests with and without reinforcement crossing the shear sliding plane. The calibration of the failure criterion explicitly accounted for the magnitude of internal confinement which is generated in the cementitious matrix in response to fibre tension. The criterion is appropriate for general purpose analysis of the stress state of SHCC, but most importantly it is used to assess the SHCC contribution to the shear strength of structural elements.

Anisotropic seabed soil failure description and three-dimensional simulation method

In order to find out the underlying effect of anisotropy on the failure characteristics from the mesoscopic mechanism, using the concept of fabric tensor and assumption of mutual mapping between isotropic space and anisotropic space, a compound stress is proposed based on the combination of ordinary stress and fabric tensor. This compound stress can be used to describe the primary anisotropic properties effectively. For the difference in the effect of stress-induced anisotropy on shear strength of various geotechnical materials in the deviatoric plane, a generalized failure criterion is proposed. This failure criterion can effectively describe various criteria forms from Von-Mises criterion to SMP criterion within a relatively large range. The hydrostatic pressure effect can also be indicated by the shape of the power function on the meridional plane. A primary anisotropy generalized failure criterion can be obtained when the compound stress is used to describe the new generalized failure criterion and the corresponding transformation stress method has been proposed. This method can consider the effect of native induced anisotropy and stress induced anisotropy on the shear strength simultaneously. The comparison between predicted and tested results shows that the proposed anisotropic generalized stress failure criterion and its transformation method can be applied to the geotechnical engineering practice simply, its rationality and applicability have also been verified.

Developing failure criteria for laceration injury of dermal tissue

Despite its importance, there is a poor understanding of human injury tolerance to trauma generally, and more specifically understanding of the mechanics of skin penetration or laceration. The objective of this analysis is to determine the failure criteria that will allow the evaluation of the laceration risk of blunt-tipped edges within a computational modeling environment. An axisymmetric tissue finite element model was set up in Abaqus 2021 to match the experimental set-up from a previous study. The model simulated the pressing of penetrometer geometries into dermal tissue, and stress and strain outputs were evaluated at the experimental failure force. Two separate nonlinear hyperelastic material models were calibrated for the dermis to data from the literature (high and low stiffness models). For both the high-stiffness and low-stiffness skin models, the failure force appears to occur near a local maximum in the principal strain. All failures occurred after the maximum strain near or at the top surface is or above 59%, with mid-thickness strain at a similar level. The strain energy density is concentrated near the edge tip for each configuration, indicating highly localized material damage at the point of loading, and increases rapidly prior to the approximate failure force. As the edge is further compressed into the tissue, the stress triaxiality near the edge contacting point decreases towards zero. This study has identified general failure criteria for skin laceration which can be implemented in a computational model. A higher risk for laceration would be indicated with strain energy density larger than 60 mJ/mm3, dermal strain larger than 55%, and stress triaxiality below 0.1. These findings were largely insensitive to the dermal stiffness and broadly applicable across different indenter geometries. It is expected that this framework may be implemented to evaluate hazardous forces for product edges, interactions with robots, and interfaces with medical and drug delivery devices.

A new generalized failure criterion and its plane strain strength characteristics

A new generalized failure criterion and its plane strain strength characteristics

Propose a generic framework for probabilistic prediction of the onset and growth of matrix cracking induced delamination in composite laminates

Matrix cracking induced delamination (MCID) is one of the catastrophic modes that can occur in composite laminates. In this paper, an efficient algorithm based on the concept of energy release rate for delamination due to matrix cracking and mode II interlaminar fracture toughness is developed and by applying this proposed framework, the reliability analysis of MCID damage is performed. The limit state function is formulated using a general and effectual failure criterion which is developed by the authors of this article, previously. To represent the performance of the proposed algorithm, the probability of the occurrence and growth of MCID in a quasi-isotropic laminate including 45°, 90°, −45° and 0° plies under different loading conditions and various stacking sequences is extracted by using first and second order reliability methods. The obtained results are verified using Monte Carlo simulation. In addition, some significant probability results are compared with several experimental data for validation of the proposed method, qualitatively. For the first time, stochastic failure envelopes called reliability based failure envelops are generated to attain deeper and clear insight about laminate random behavior under MCID mode. The effect of some variables such as the ply thickness, different stress level and stress states and matrix cracking density on the probability of occurrence and growth of MCID is investigated.

Building an Integrated Drilling Geomechanics Model Using a Machine-Learning-Assisted Poro-Elasto-Plastic Finite Element Method

SummaryThe petroleum industry has long relied on predrilling geomechanics models to generate static representations of the allowable mud weight limits. These models rely on simplifying assumptions such as linear elasticity, a uniform wellbore shape, and generalized failure criteria to predict failure and determine a safe mud weight. These assumptions lead to inaccurate results, and they fail to reflect the effect of different routing drilling events. Thus, this paper’s main objective is to improve the process for predicting the wellbore rock failure while drilling. This work overcomes the limitations by using a new and integrated modeling scheme.Wellbore failure prediction is improved through the use of an integrated modeling scheme that involves an elasto-plastic finite element method (FEM) model, machine learning (ML) algorithms, and real-time drilling data, such as image logs from a logging while drilling (LWD) tool that accurately describes the current shape of the wellbore. Available offset well data are modeled in the FEM code and are then used to train the ML algorithms. The produced integrated model of FEM and ML is used to predict failure limits for new wells. This improved failure prediction can be updated with the occurrence of different drilling events such as induced fractures and wellbore enlargements. The values are captured from real-time data and reflected in the integrated model to produce a dynamic representation of the drilling window.The integrated modeling scheme was first applied to laboratory experimental results to provide a proof of concept and validation. This application showed improvement in rock-failure prediction when compared with conventional failure criteria such as Mohr-Coulomb. Also, offset-well data from wireline logging and drilling records are used to train and build a field-based integrated model, which is then used to show that the model output for a separate test well reasonably matches the drilling events from the test well. Application of this integrated model highlights how the allowable mud-weight limits can vary because drilling progresses in a manner that cannot be captured by the conventional predrilling models.As illustrated by a field case, the improvement in failure prediction through this modeling scheme can help avoid nonproductive time events such as wellbore enlargements, hole cleaning issues, pack-offs, stuck-pipe, and lost circulation. This efficiency is to be achieved by a real-time implementation of the model where it responds to drilling events as they occur. Also, this model enables engineers to take advantage of available data that are not routinely used by drilling.

Nonlinear Shear-Strength Reduction Technique for Stability Analysis of Uniform Cohesive Slopes with a General Nonlinear Failure Criterion

Abstract This paper develops a nonlinear shear-strength reduction technique for analyzing the stability of uniform slopes with the general nonlinear failure criterion. To incorporate the nonlinear ...

A failure criterion revision method for composite materials

Failure criterion predictions often have substantial errors due to the complexity of failure mechanism or different material behaviors, especially composite failure. In this study, an example of delamination is employed to demonstrate the general failure criterion revision of composites. In the present research, the failure function can be raised to a higher order, and also be reduced to a lower one, by fitting the exponents of failure criterion. This method can be easily used to describe the observed, experimented, or computed data, particularly with no law or no rules. Further, the importance of this exponent revision is amplified when the failure surface becomes more complicated. The proposed approach is also to define and calculate the failure criteria of multiplying laminates.

A general failure criterion for soil considering three-dimensional anisotropy

Abstract This paper proposes a generalized three-dimensional (3D) failure criterion for cross-anisotropic soils based on the spatially mobilized plane (SMP) criterion. In the proposed criterion, the anisotropic property of soil is considered by introducing a novel modification stress tensor, in which the angle between the principal stress and the soil depositional direction serves as a basic variable. Taking advantage of the SMP criterion, the proposed anisotropic criterion is subtly extended into a 3D version. The proposed criterion only involves two friction angles, φ v and φ h , which are determined by triaxial compression test along and perpendicular to the depositional direction, respectively. To account for the effects of the depositional direction, two special modification stress tensors regarding different depositional conditions (vertical and inclined) are discussed in this study. Comparisons between the predictions from the proposed strength criterion and the observations of the true triaxial tests on four cross-anisotropic soil samples show that the proposed generalized failure criterion can well capture both the cross-anisotropic behaviors and the 3D strength of cross-anisotropic soils.

Assessment of Fatigue Induced Pad Cratering With a Universal Expression of Printed Circuit Board Fatigue Resistance

Abstract Repeated loading is an important reason to cause pad cratering fatigue failure in ball grid array (BGA) device in printed circuit board (PCB) assembly. For industry application, the board level drop test is commonly applied to evaluate the pad cratering fatigue strength under the repetitive drop loading. Although this testing method is consistent with the actual service condition of BGA-PCB assembly, it is extremely time consuming in the testing operation and expensive in costs. Another fatigue evaluation testing method for BGA-PCB assembly is the board level cyclic bending test. Compare with the board level drop test, this testing method can be handled by universal testing machine automatically without manual operation during the testing process. In consequence, the cyclic bending test has the merits of simple, fast, and low costs, and it is always desirable to evaluate the repeated drop life of pad cratering with cyclic bending test. This research proposes a correlation between the cyclic bending and repetitive drop test in BGA-PCB assemblies. With assistance of finite element method, the equivalent cyclic bending testing conditions of drop tests are developed. The experimental validation is also conducted to prove accuracy of the correlation. From the analysis of finite element method and experiments, both cyclic bending tests and repetitive drop tests agree with the same strain–number of cycle (S–N) curve. This means the S–N curve can be treated as a generalized failure criterion of fatigue induced pad cratering. The conclusion is crucial for reliability design phases to prevent the pad cratering fatigue failure.

Incorporating scale effect into a failure criterion for predicting stress-induced overbreak around excavations

The evaluation of the depth of brittle failure around excavations is of major importance in order to optimize the design of underground excavations and ensure the safety of workers and equipment. The current proposed approaches to evaluate it are related to a single scale of study (intact rock or rock mass scale). Therefore, they are scale-dependent, and cannot be applied for all excavation diameter. In this paper, a generalized failure criterion including the scale effect for predicting stress-induced overbreak around excavations is developed. This failure criterion is based on the damage initiation relation (σ1= Aσ3+ Bσc). The scale effect is included into it through a relation proposed to evaluate the B parameter and depending on the scale of study. The fit parameters of the relation proposed have been defined considering a database at both rock mass and intact rock scales arising from a literature review. For intact rock scale, the B parameter is defined as a function of the diameter of the excavation, expressed following a potential form. For rock mass scale, the B parameter is defined equal to 0.35, regardless the diameter of the excavation. Based on the proposed B parameter relation, the depth and extension of the brittle failure around excavations can be evaluated for any scale of study.

Reliability back analysis of landslide shear strength parameters based on a general nonlinear failure criterion

The shear strength parameters of a sliding surface are important parameters for the stability evaluation and engineering design of a landslide. To consider the randomness, uncertainty and the nonlinear characteristics of the geotechnical, the reliability back analysis method of determining shear strength parameters of a landslide based on nonlinear Mohr-Coulomb failure criteria is proposed in this study. By analyzing a slope with linear failure surface, the feasibility and validity of the proposed method are discussed in an engineering case. The proposed method provides a new choice and reference for the determination of the shear strength parameters of the sliding surface of a landslide.

Nonlinear modeling of the failure of a graphite epoxy under a three-point bending test

The application of modeling theories and the choice of failure criteria are difficult in part because they are too varied and must be validated by biaxial tests, which are expensive to be performed. This article is devoted to the nonlinear modeling and failure criteria which are employed in the design and analysis of anisotropic materials. Indeed, in this work, a study of the macroscopic and microscopic behavior of a graphite epoxy under a three-point bending test is conducted, and the successive failures are also predicted. Experimentally, the damage progression and the effect of geometrical parameters are followed and identified in detail. The analytical modeling is based on a recently developed approximation for isotropic materials. This approximation is also valid for the studied quasi-isotropic laminated composite. A software program has been elaborated for the application of the most general failure criteria. The results obtained by this analytical modeling show a good correlation with those of the experimental study.

A review and application of the failure criteria on a graphite epoxy under three-point bending test

The application of failure criteria are difficult partly because they are too various and must be validated by biaxial tests, which are expensive to be achieved. In this work, an analytical modeling based on a software program has been elaborated for application of the most general failure criteria and prediction of successive failure. Finally, the results obtained by this analytical modeling show a good correlation with those carried out by experimental study.

Predicting the behavior of unbound granular materials under repeated loads based on the compact shakedown state

Abstract The behavior of unbound granular material under repeated loads primarily depends on the nature and arrangement of constituent particles, particle size and shape. However, very few analytical models are available for predicting the behavior of unbound granular material under repeated loads. This paper presents a generalized failure criterion with a non-associated flow rule which uses from the concept of compact shakedown state for predicting the stress–strain behavior of unbound granular material. At the compact shakedown state, the response of the unbound granular sample to a stress change is reversible and behaves as an elastic material. In an extension to original CANAsand constitutive model, two concepts namely critical state and compact shakedown state play paramount roles as all of the moduli and coefficients are related to these states. In contrast to the critical state, the unbound granular material samples do not experience any plastic deformation at the compact shakedown state and behaves as a purely elastic material and the response to a stress change is reversible. For stress reversal two additional concepts as reflected plastic potential and bounding surface are employed which distinguishes between virgin loading and secondary loading. The extended model is examined by simulating different typical drained tests in conventional tri-axial tests. The applicability of the present model is evaluated through comparisons between the predicted and the measured results.

A novel triaxial failure model for adhesive connections in structural glass applications

Structural adhesive connections for glass applications have been widely investigated in the past years, because of their enhanced mechanical performance when compared to bolted connections. However, due to the lack of established design methods and failure criteria, laboratory tests must always be performed, when adhesive connections are used in real-world structural applications. Because of the above, this work presents the analytical development of a Generalized Triaxial Model (here called GTM) that describes a novel failure criterion for adhesive materials in structural glass applications. This is done developing a generalized triaxial model defined over the three-dimensional stress space, which accounts for the non-linear effects of strain rate and temperature variation. The main output of this work is a five-dimensional formulation that allows to account for a generic stress state by a governing equation expressed as a function of the three-dimensional stress tensor. Both deviatoric and hydrostatic energetic components are taken into consideration by means of a non-linear function of the two contributions. The governing equation is represented in the stress space by a revolution surface that is axial-symmetric with respect to the hydrostatic axis, thus independent of the third stress invariant. The proposed model is suitable for isotropic materials and it is here applied to SentryGlas and TSSA, two adhesive materials used in structural glass applications, for which extensive test campaigns have been performed but for which no failure criteria are available yet in literature. Firstly, the proposed model is analytically compared to other existing general failure criteria. It is shown that some of the existing models that can be found in literature can be seen as a particular case of the proposed model. Then, the model is compared with the experimental results under different loading conditions, strain rates and temperatures. The results are found to be in line with the model predictions for both materials. Additional tensile-torsion tests are also performed to validate the proposed model at varying values of the hydrostatic angle.

Nonlinear Viscoelasticity and Generalized Failure Criterion for Polymer Gels

Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we describe this scenario for a model protein gel using an integral constitutive equation built upon the linear and the nonlinear viscoelastic properties of the gel. We show that this formalism predicts quantitatively the gel mechanical response in shear start-up experiments, up to the onset of macroscopic failure. Moreover, we couple the computed stress response with Bailey's durability criterion for brittle solids in order to predict the critical values of the stress σc and strain γc at failure. The excellent agreement between theory and experiments suggests that failure in this soft viscoelastic gel is a Markovian process and that Bailey's failure criterion extends beyond hard materials such as metals, glasses, or minerals.

Equivalent Stress Tensor and Anisotropic Failure Criterion of Soils

Experimental evidence shows that the strength of geomaterials is significantly influenced by the inherent anisotropy, the intermediate principal stress and the stress direction. To measure the joint effect of the fabric tensor and the stress tensor, a second-order tensor named the equivalent stress tensor is extracted from the equilibrium equation of the soil-skeleton. As the magnitude and direction of the effective stress together with the microscopic characteristics of anisotropy are enrolled in the equivalent stress tensor, the modelling process of anisotropic failure criterion with the application of the equivalent stress tensor is proposed. On this basis, a general 3D failure criterion of anisotropic geomaterials is formulated based on the SMP criterion, of which all introduced parameters can be conveniently determined by conventional laboratory tests. Comparison with experimental results of various stress paths from literatures claims that the anisotropic failure criterion is able to capture the strength anisotropy in torsional shear tests. Further discussion is done on the possible application of the equivalent stress and the probable improvement of the new criterion to address other models.

Failure Theory/Failure Criteria for Fiber Composite Laminates

Failure criteria are derived for the case of a quasi-isotropic laminate and for the more general case of orthotropic laminates. The former requires two calibrating failure properties obtained directly from laminate testing and the latter requires five standard experimental measurements for its calibration. Then the quasi-isotropic failure theory is taken much further, also admitting full calibration by only the two composites tow failure properties, the associated unidirectional tensile, and compressive strengths. The theoretically predicted failure envelope for the quasi-isotropic laminate is favorably compared with some comprehensive testing data. As a related matter, the general failure criteria for unidirectional fiber composites are also reviewed.