Classical Failure Criteria Research Articles

Experimental and numerical investigation on folding stable state of bistable deployable composite boom

The bistable deployable composite boom (Bi-DCB) can realize the bistable function by storing and releasing strain energy, which has a good application prospect in the aerospace field. In this paper, the folding stable state of the Bi-DCB was investigated using experimental and numerical approaches. Using the vacuum bag method, six Bi-DCB specimens were prepared. Bistable experiments of Bi-DCB specimens were conducted and linear fitting with Archimedes’ helix was performed to determine the folding stable configuration. In addition, two Finite Element Models (FEMs) were established for predicting the folding stable state of the Bi-DCB. Two classical failure criteria were utilized to analyze the stress level of the folding stable state of the Bi-DCB. Numerical results of two FEMs agreed well with experimental results, including the bistable deformation process and the folding stable state.

Failure prediction for fiber reinforced polymer composites based on virtual experimental tests

A novel virtual experimental testing methodology that utilizes virtual microstructures representative of genuine fiber distribution, is devised to micromechanically simulate and scrutinize the inter-fiber failure of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The experimentally identified nonlinear behavior of the matrix is incorporated by utilizing the Drucker-Prager plasticity model. The interaction behavior between fiber-matrix interfaces, including delamination and friction, is represented by means of a cohesive interaction approach. The results of virtual testing demonstrate that interfacial parameters and the epoxy properties exert considerable influences on the predicted macroscopic responses under individual loading cases. Additionally, the interface and epoxy material properties are inversely determined through virtual testing analysis assisted by experimental results. Furthermore, the validated virtual testing method is utilized to obtain the inter-fiber failure envelope of the composites. The predictions are then compared with those theoretically derived from classical failure criteria. The current comparative studies indicate that the existing classical failure criterion exhibits limited predictive ability with computational data.

Numerical investigation on the mechanical behaviors of 2D woven composites under complex in-plane stress states

Using finite element method (FEM), the mechanical behaviors of 2D woven composites with different weave structures are investigated with considering the complex in-plane stress states. Periodic boundary conditions for arbitrary off-axis loading scenarios are established, and a progressive damage model based on Linde criterion is proposed, which is subsequently validated by the previous experiments. In addition, the failure envelopes predicted by classical failure criteria are compared to the results obtained by FEM. The effects of woven structures on elastic properties and failure behavior are also discussed, which demonstrates that the plain woven composites have inferior mechanical performance than twill and satin woven composites. Based on the assessment of the failure criteria, this study provides recommendations for selecting relevant failure criteria to anticipate mechanical properties under various loading conditions. The findings in this paper are expected to encourage the development of damage constitutive models and their engineering applications for 2D woven composites.

A review on micromechanical modelling of progressive failure in unidirectional fibre-reinforced composites

The recent decades have seen various attempts at the numerical modelling of fibre-reinforced polymer (FRP) composites in the aerospace, auto and marine sectors due to their excellent mechanical properties. However, it is still challenging to accurately predict the failure of the composites because of their anisotropic and inhomogeneous characteristics, multiple failure modes and their interaction, especially under multiaxial loading conditions. Micromechanics-based numerical models, such as representative volume elements (RVEs), were developed to understand the progressive failure mechanisms of composites, and assessing existing failure criteria. To this aim, this review paper summarises the development of micromechanics-based RVE modelling of unidirectional (UD) FRP composites reported in the literature, with a focus on those models developed using finite element (FE) and discrete element (DE) methods. The generation of fibre spatial distribution, constitutive models of material constituents as well as periodic boundary conditions are briefly introduced. The progressive failure mechanisms of UD FRP composites simulated by RVEs under various loadings are discussed and the comparison of failure envelopes predicted by numerical results and classical failure criteria are reviewed.

An implicit integration algorithm based on invariants for isotropic elasto‐plastic models of the Cosserat continuum

AbstractA Finite Element (FE) procedure based on a fully implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. The integration algorithm is suitable for yield and plastic potential surfaces with general shape in the deviatoric plane. The key element of the integration scheme is the spectral decomposition of the stress tensor, which is achieved, despite the lack of symmetry, because of the mathematical structure of the yield function and the set of invariants chosen as independent variables. It is also shown that the choice of invariants enables considerable mathematical simplifications, which result in the reduction of the system of equations and unknowns of the elasto‐plastic problem from 19 to 1, and to rigorously handle the discontinuity at the apex of the surfaces. The algorithm has been implemented in a proprietary FE programme, and used for the constitutive model recently proposed by the same authors in this journal for the Cosserat continuum, which allows to set various classical failure criteria as yield and plastic potential surfaces. Numerical analyses have been conducted to simulate a biaxial compression test and a shallow strip footing resting on a Tresca, Mohr–Coulomb, Matsuoka–Nakai and Lade–Duncan soil. The benefits of the Cosserat continuum over the Cauchy/Maxwell medium are discussed considering mesh refinement, non‐associated flow and softening behaviour.

A numerical prediction of failure probability under combined compression-shear loading for unidirectional fiber reinforced composites

Microbuckling (MB) is the dominant failure mode in unidirectional fiber reinforced polymers (FRPs) under predominantly compression loads. MB is highly sensitive to material imperfections and nonlinear material behavior. Material imperfections are spread in the form of fiber misalignment in the volume of the material. Because of high sensitivity of MB failure to the fiber misalignment, the MB strength shows uncertainty. It has been shown in the literature that the nature of the misalignment in FRPs is correlated random, where the misalignment of a fiber depends on the other fibers in its surroundings. To represent the misalignment in numerical models for the prediction of MB strength while preserving the spatial correlation information, the spectral representation method is employed in this investigation. For this purpose spectral densities were calculated for measured distributions of the fiber misalignment using computed tomography scans on specimens. This information was subsequently used to generate realistic distributions of the fiber misalignment in numerical modeling of FRPs for prediction of MB strength. Quantification of uncertainty in MB failure is essential for reliable design practices. Therefore, the current investigation aims for a probabilistic prediction of MB failure under axial compression and combined compression-shear loads. Different model series, each containing a large number of realizations, were developed based on spectral densities calculated from the measurements of the fiber misalignment from different specimens. The resulting distributions of strengths under the axial compression load case from these model series are compared and a suitable model series was chosen for further analysis. The stress–strain response under different combinations of combined compression-shear loads is discussed. A comparison of numerically predicted strengths against experimentally obtained results under the axial compression loads is included. Since the sizes of the model and the experimental specimen were different, this comparison was performed on the basis of a scaling law for the compression strength. Finally, the numerically determined probabilistic failure envelopes in stress and strain spaces are presented with lower percentiles of distributions of failure. The failure enveloped are also compared against classical failure criteria from the literature to highlight the limitations of the classical criteria.

A general-purpose, inelastic, rotation-free Kirchhoff–Love shell formulation for peridynamics

We present a comprehensive rotation-free Kirchhoff–Love (KL) shell formulation for peridynamics (PD) that is capable of modeling large elasto-plastic deformations and fracture in thin-walled structures. To remove the need for a predefined global parametric domain, Principal Component Analysis is employed in a meshfree setting to develop a local parameterization of the shell midsurface. The KL shell kinematics is utilized to develop a correspondence-based PD formulation. A bond-stabilization technique is employed to naturally achieve stability of the discrete solution. Only the mid-surface velocity degrees of freedom are used in the governing thin-shell equations. 3D rate-form material models are employed to enable simulating a wide range of material behavior. A bond-associative damage correspondence modeling approach is adopted to use classical failure criteria at the bond level, which readily enables the simulation of brittle and ductile fracture. Discretizing the model with asymptotically compatible meshfree approximation provides a scheme which converges to the classical KL shell model while providing an accurate and flexible framework for treating fracture. A wide range of numerical examples, ranging from elastostatics to problems involving plasticity, fracture, and fragmentation, are conducted to validate the accuracy, convergence, and robustness of the developed PD thin-shell formulation. It is also worth noting that the present method naturally enables the discretization of a shell theory requiring higher-order smoothness on a completely unstructured surface mesh.

Numerical Prediction of Failure in Unidirectional Fiber Reinforced Composite

Fiber-reinforced polymer composites exhibit orthotropic mechanical properties and particularly low strength in the out-of-plane direction. The use of classical failure criteria that consider transverse isotropy to evaluate these composite materials implies an overestimation of their out-of-plane strength, which could lead to a nonconservative and even catastrophic design. The Molker failure criteria developed for orthotropic materials consider the LaRC05 failure modes as a basis, with two additional failure modes for the out-of-plane direction of noncrimp fiber (NCF)-reinforced composites. Given the similarity in configuration and orthotropic behavior of unidirectional fiber fabric reinforced composites to NCF-reinforced composites, Molker failure criteria are implemented and applied in this research to determine the initiation of out-of-plane failure in unidirectional fiberglass fabric composites. The criteria are programmed in the form of a module coupled to a constitutive model available in a finite element method (FEM) package. Then, the mechanical properties and failure parameters of the unidirectional fiber-reinforced composite are determined. Model validation is accomplished by comparing numerical and experimental results of out-of-plane failure in a corrugated panel. In addition, several failure criteria used in unidirectional fiber-reinforced composite that consider transverse isotropy are evaluated. The results of critical load at the onset of transverse out-of-plane failure obtained by using the Molkerorthotropic criterion prove to be superior in accuracy compared to those obtained with the criteria commonly applied to this type of materials.

Effects of Th doping on mechanical properties of U<sub>1–</sub><i><sub>x</sub></i>Th<i><sub>x</sub></i>O<sub>2</sub>: An atomistic simulation

Since thorium (Th) owns high conversion ratio in thermal neutron spectrum, high melting temperature, high thermal conductivity and good corrosion resistance in high-temperature water, it can be doped into UO<sub>2</sub> based fuel to initiate the fission reaction, and improve the physical properties of UO<sub>2</sub>. Owing to the challenging experimental conditions and technologies, molecular dynamics (MD) simulations are conducted to investigate the influences of Th doping on the mechanical properties of U<sub>1–</sub><i><sub>x</sub></i>Th<i><sub>x</sub></i>O<sub>2</sub>. The phase transition from initial fluorite structure to the metastable scrutinyite phase when loading along the [001] direction is observed, which accords well with the previous density functional theory calculations. However, if U<sub>1–</sub><i><sub>x</sub></i>Th<i><sub>x</sub></i>O<sub>2</sub> is loaded along the [111] direction, only brittle fracture is observed. It is found that both the elastic modulus and fracture stress decrease linearly with elevating temperature but the fracture strain increases. As the Th concentration increases from 0 to 0.55, the elastic modulus first decreases and then increases; if the Th concentration is larger than 0.1, the fracture stress increases and the fracture strain decreases monotonically. The cracks are nucleated with an angle of 45º to the loading direction, propagate rapidly, and are characteristic of brittle fracture, which accords well with the classical failure criteria and experimental results for brittle materials. By comparison, the uniaxial tensile loading is also performed for polycrystalline U<sub>1–</sub><i><sub>x</sub></i>Th<i><sub>x</sub></i>O<sub>2</sub>. It is found that the elastic modulus and fracture stress decrease as the temperature increases. However, the elastic modulus is not sensitive to the Th concentration and the fracture increases as the Th concentration increases. The brittle intergranular fracture is observed in each of all polycrystalline samples. The obtained physical parameters are useful for designing the fuels in nuclear reactors.

Early stage crack detection in mechanically joined steel/aluminum joints by condition monitoring

Abstract Monitoring systems for machines, plants, materials and equipment are increasingly used in production processes. These online condition monitoring systems can detect damage or excessive loads at an early stage and can drastically reduce or prevent long downtimes of plants and machines as well as high repair and maintenance costs. This paper depicts a method for online crack detection with pattern recognition methods for specimens joined by self-pierce riveting under cyclic load in fatigue tests (laboratory application). A software specially conceived for this application was developed. This software, AnrissMF, uses active acoustic testing with a structure-borne sensor to detect cracks in the joints at a very early stage. It is shown in this paper that this software can detect cracks much earlier than classical failure criteria for joints (i. e. before any drop in stiffness or frequency is observed). Furthermore, the successful application of software AnrissMF for online crack detection during the fatigue strength test is presented.

Early stage crack detection in mechanically joined steel/aluminum joints by condition monitoring

Abstract Monitoring systems for machines, plants, materials and equipment are increasingly used in production processes. These online condition monitoring systems can detect damage or excessive loads at an early stage and can drastically reduce or prevent long downtimes of plants and machines as well as high repair and maintenance costs. This paper depicts a method for online crack detection with pattern recognition methods for specimens joined by self-pierce riveting under cyclic load in fatigue tests (laboratory application). A software specially conceived for this application was developed. This software, AnrissMF, uses active acoustic testing with a structure-borne sensor to detect cracks in the joints at a very early stage. It is shown in this paper that this software can detect cracks much earlier than classical failure criteria for joints (i. e. before any drop in stiffness or frequency is observed). Furthermore, the successful application of software AnrissMF for online crack detection during the fatigue strength test is presented.

Computational micromechanics model based failure criteria for chopped carbon fiber sheet molding compound composites

Chopped carbon fiber sheet molding compound has a great potential in lightweight automotive, marine, and aerospace applications. One of the most challenging tasks is to predict the failure strength of the material due to its anisotropy and heterogeneity, as well as complex stress states in real-world working conditions. In this paper, a novel constitutive model of carbon fiber chip is proposed to capture the pre- and post-failure behaviors under different loading modes. On this basis, we propose a new computational micromechanics model, which is calibrated and validated by uniaxial tensile, compressive, and in-plane shear experiments. Furthermore, a set of microstructures representative volume element (RVE) models under complex loading conditions are reconstructed to understand the relationship between the microstructure characteristics and the failure envelopes. Finally, several modified versions of classical failure criteria are proposed for anisotropic materials with consideration of the fiber orientation tensor. The modified Tsai-Wu failure criterion, which shows the best accuracy among all failure criteria, is highlighted in the comparative study.

A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker-Prager, Tresca, Mohr-Coulomb, Bresler- Pister and Willam-Warnke.

An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker-Prager, Tresca, Mohr-Coulomb, Bresler-Pister and Willam-Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr-Coulomb criteria-an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.

Deep Contact Strength of Surface Hardened Gears

This article is devoted to the analysis methods for assessing the load capacity of gears hardened by surface chemical-thermal treatment (CTT), which are characterized by structural and chemical heterogeneity. The leading type of failure is determined by several factors, the main of which are the surface and deep layer properties of the material, which fundamentally differ in the energy and structural state. Intercrystalline fracture mechanisms predominate in the surface layers and transcrystalline in the core. For these cases, the classical failure criteria of Mohr, Tresca, and Mises lead to significant errors. Therefore, the bearing capacity of the layer component is investigated by the generalized criterion of the limit state of the Pisarenko-Lebedev structurally inhomogeneous material, considering changes in its plastic properties due to surface hardening. The reliability of predicting the level of bearing capacity of surface hardened steel parts, such as gears, was significantly improved. The influence of the plasticity parameter on the level of bearing capacity for various types of CTT is estimated. Calculations using the presented model show that for alloy steels with a Ni content up to 1%, the safety coefficient can be limited to 1.2, which will increase the bearing capacity by 25–27%.

A semi-Lagrangian constitutive correspondence framework for peridynamics

Lagrangian formulations, in which material models are established upon a mapping from a deformed domain back to an undeformed reference configuration, have traditionally been employed in most previous developments of the peridynamic theory. In this paper, a semi-Lagrangian constitutive framework for peridynamics is proposed, in which peridynamic material point interactions depend only on their current properties (e.g. position and stress values) in the deformed configuration. A nonlocal version of the velocity gradient is proposed to determine the Cauchy stress rate, using local constitutive theories, as an intermediate quantity in computing peridynamic bond forces. It is shown that a pure state-based peridynamic approach would involve material instabilities. A bond-associated formulation is presented to benefit from both bond-based and state-based views, resulting in an enhanced stability. A bond-associated, correspondence damage modeling is introduced to incorporate classical failure criteria in a convenient way. The proposed framework opens up new pathways in modeling extreme events, where excessive material deformation and damage make the Lagrangian formulation unsuitable. Capabilities of the new theory is showcased in a handful of illustrative scenarios.

Failure criteria of unidirectional carbon fiber reinforced polymer composites informed by a computational micromechanics model

Failure prediction for carbon fiber reinforced polymer (CFRP) composites has been a longstanding challenge. In this study, we address this challenge by first applying a well-established computational micromechanics model based on representative volume element to predict the failure envelopes of unidirectional (UD) CFRP composites. Then, these failure envelopes are compared with the classical failure criteria. We have evaluated the performances of these failure criteria and identified the aspects for further improvement in their accuracies for the UD CFRP composites studied herein. Based on the failure mechanisms from computational analyses and the comparisons between predicted failure envelopes and classical failure criteria, a new set of homogenized failure criteria is proposed. The newly proposed failure criteria show significant improvement according to our computational and experimental results. Furthermore, we have compared the proposed failure criteria with existing experimental data and computational results available in the literature for different types of composites. Good agreements are generally observed.

Experimental Analysis and Failure Criterion of Plain Concrete Subjected to Biaxial Loading under Fixed Lateral Loading

By using a rock true triaxial apparatus hydraulic servo machine, biaxial loading experiments including biaxial compression‐compression and biaxial compression‐tension with fixed lateral loading on plain concretes were conducted and the stress‐strain curves of plain concrete under various stress ratios were obtained. After determining the peak principal stress, the damage modes of plain concrete under various stress ratios were analyzed and the law of strength in the principal stress direction was studied as well. The experimental findings show that, under the fixed lateral loading, the failure modes of plain concrete under biaxial compression‐compression and biaxial compression‐tension are very similar to those under the equal proportional loading, but with higher amplitude of variation. In this paper, Kupfer’s classical failure criterion was applied to verify the experimental data and the predicted biaxial loading on plain concrete under fixed lateral loading and was regarded as relatively conservative. Meantime, based on Kupfer’s failure criterion and octahedral stress space, two different failure criteria had been proposed and verified. The results show that the proposed failure criteria have good applicability. The failure mechanism under fixed lateral loading was discussed and compared with that under the equal proportional loading method. This research is meaningful to plain concrete engineering application and calculation.

Analysis of the failure of H240LA steel sheets subjected to stretch-bending conditions

Industrial sheet metal forming processes with certain complexity involve intrinsically non-linear strain paths, abrupt changes in the local strain ratio (β) due to successive stages during the manufacturing operation and/or the existence of strain/stress gradients through the sheet thickness due to the simultaneous action of stretching and bending. Under these situations, both the use of classical failure criteria assuming a uniform strain/stress distribution across the sheet thickness and the use of strain-path dependent metrics, such as the conventional FLC (Forming Limit Curve), for assessing sheet formability are highly questionable. In this work a failure model for stretch-bending which combines both the use of a path-independent formability diagram, based on the polar equivalent plastic strain curve (epFLC), along with different rules to account for the influence of the stress/strain gradient across the sheet thickness, particularly the Mid-Plane Rule (MPR), Concave-Side Rule (CSR) and Convex-Side Rule (CxSR), is explored. Their capabilities to predict failure by necking in a series of stretch-bending tests over H204LA steel sheets of 1.2 mm thickness are discussed in the light of experimental results. To this end, a 3D calibrated numerical model was used to precisely describe the realistic distribution of stresses/strains across the sheet thickness.

Experimental study of the size effect on transverse cracking in cross-ply laminates and comparison with the main theoretical models

Transverse cracking of off-axis plies is typically the first step of some failure mechanisms in long fiber reinforced laminated composites. It is well known that the off-axis ply thickness affects strongly the strain level which this ply is able to withstand without cracking. Experimental evidences show that this critical strain level increases strongly with decreasing ply thickness for the thinnest plies, confirming a clear size effect. This fact could be used to inhibit transverse cracking with the use of the recently developed ultra-thin plies. However the classical failure criteria for composites are not able to predict this size effect. From the first tests in the 1970s, several models with very different hypotheses were proposed to predict this size effect. Surprisingly there is still not a clear consensus in the scientific community about which is the adequate model, though their fundamentals are radically different. In this work an extensive test campaign is carried out on self-similar [0/90]s cross-ply laminates of AS4/8552 carbon/epoxy. The size effect is evaluated spanning a broader spectrum of thicknesses than in the tests presented in the literature until now, in order to explore the range of thicknesses where the differences between predictions of the main theoretical models are larger. In spite of the inherent dispersion in the experimental results, the comparison shows that the purely stress-based criteria underestimates the apparent strength of the off-axis ply. The other models predict very similar results, particularly for the thinnest laminates, with slight underestimations or overestimations, depending on the model.

An extended modified Cam-Clay yield surface for arbitrary meridional and deviatoric shapes retaining full convexity and double homothety

This paper presents a new yield function, defined in terms of stress invariants and suitable for isotropic geomaterials. It is a generalisation of that of the modified Cam-Clay (MCC) model and as such it retains all the mathematical advantages of the original formulation, which are particularly convenient for the numerical integration of the constitutive law. In addition the proposed function is capable of providing a wide range of shapes and it is therefore suitable for defining both the yield and the plastic potential surfaces. As compared to the original MCC ellipse, one additional parameter is introduced for defining the shape of the meridional section, which conveniently controls also the relative position of the normal compression and critical state lines. In the deviatoric plane the function not only provides the exact shape of classical failure criteria, such as von Mises, Drucker–Prager, Matsuoka–Nakai, Lade–Duncan, Tresca and Mohr–Coulomb, but it is also capable of rounding the hexagons of the last two criteria with a continuity of class at least C2 required for achieving a quadratic convergence of the integration scheme. The new function has an unrestricted domain of definition, expands/shrinks homothetically with respect both to the origin of the stress space and to its centre and is characterised by convexity for any level set. The last two important features were obtained by applying a convexification technique proposed by the authors elsewhere.