Mixed Mode Loading Research Articles

Glass/epoxy fiber orientation effects on translaminar fracture toughness under Mixed mode(I/II) load using FPB specimen

To study glass/epoxy fiber orientation effects on translaminar fracture toughness under Mixed mode(I/II) load using asymmetric Four Point Bend specimen. Fracture toughness values for different fiber-oriented glass/epoxy laminates under Mixed modes are compared with unidirectional glass/epoxy laminates. Specimens were fabricated using hand layup technique with (0/45)° and (0/90)° fiber oriented glass fiber. The experimental study was conducted for 6 crack positions varying from 0 to 1 with an increment of 0.2 for Four Point Bend specimen. The specimens were tested under universal testing machine to obtain peak loads and further evaluate fracture toughness. The experimental test results show fracture toughness can be increased by orienting the fiber in the laminate. Fracture toughness is highly dominating for (0/90)° fiber-oriented laminates compared to 0° and (0/45)° glass/epoxy laminates.

A cohesive zone model to predict fatigue-driven delamination in composites

A cohesive zone model is proposed to analyse composite delamination propagation under high-cycle fatigue loading. A new method to compute the strain energy release rate at any point within the element fatigue life cycle range is presented. The proposed scheme is based on the J-integral method evaluated at an estimated position of the crack-tip within the element, instead of the element integration points. Furthermore, a new fatigue damage evolution law is proposed to account for the unwanted quasi-static damage during the element fatigue degradation process. The model prediction capabilities were verified against experimental data available in the literature and theoretical solutions using a double cantilever beam configuration for mode I loading, four-point end-notched flexure configuration for mode II loading, and mixed-mode bending configuration for mixed-mode loading. The simulations were performed at both constant and variable amplitude loading. The numerical predictions obtained using the proposed model correlated very well with literature’s experimental data.

Mixed-mode I + II tensile fracture analysis of thermally treated granite using straight-through notch Brazilian disc specimens

The destruction and fracture failure of heat-treated rock structures have been major issues in the underground engineering, such as disposal of highly radioactive nuclear waste, deep mining and exploitation of geothermal resources. Although several literatures have focused on studying the mode I fracture toughness and mode I fracture characteristics of heat-treated rocks, studies of the thermal effect on the mixed-mode fracture toughness and mixed-mode fracture characteristics are rare. Additionally, there is a lack of systematic study to analyse the fracture characteristics of heated rocks on theoretic aspects. In this paper, lots of mixed-mode I + II fracture tests were conducted on a heat-treated granite using straight-through notch Brazilian disc specimens. A total of six specimen groups (25, 100, 200, 400, 600 and 800 °C) and four loading mixities (Mode I loading, mode II loading and two mixed-mode loadings) are selected to apply the fracture tests. The results show that temperature treatment can both significantly affect the brittleness and the mixed-mode fracture toughness of the granite, but the fracture initiation angle is not sensitive to high temperature. The mode I fracture toughness and mixed-mode fracture toughness develop similar trend with increasing treatment temperature. The theoretical fracture models can be effectively applied to predict variations of the mixed-mode fracture parameters. This research also indicates that fracture parameters at high temperature are likely to be predicted by the well-known fracture criterion by only taking the rock physical and mechanical parameters at natural temperature. This work could provide a reference to the research on the mechanical properties and fracture failure of rocks during restoring of post-fire rock structures or hydraulic fracturing of hot dry rocks.

Experimental and numerical investigation on fatigue crack growth behavior of commercial pure titanium under I-II mixed mode loading at negative load ratios

With the increase of design and application parameters for pressurized structures, the mixed mode fatigue crack growth (FCG) behavior has become a concerned problem in the field of structural integrity. In order to understand FCG behavior of I-II mixed mode crack growth at negative load ratios, an improved compact tensile shear (CTS) specimen of commercial pure titanium is taken to study the effects of load ratio and loading angle on I-II mixed mode FCG behavior through experiments and finite element method (FEM), which mechanism is discussed in depth as well. The contribution of mode I and mode II crack growth driving forces to I-II mixed mode FCG is analyzed. The changes of crack fracture criterion and the mechanism of crack growth in I-II mixed mode FCG process are revealed, and the competition relationship between two crack closure mechanisms of I-II mixed mode crack at negative load ratios is explained. An improved fatigue crack growth rate (FCGR) model that can make I-II mixed mode FCGR normalized is proposed by considering both the crack closure and the crack fracture criterion eventually.

Mixed-mode fracture response of anti-symmetric laminates: Experiments and modelling

Multidirectional laminates are very often used in advanced structures. However, the existing data in the literature regarding their fracture response is not conclusive. In this work, the fracture response of a +45∘//−45∘ interface is investigated under remote mixed mode loading and compared to a 0∘//0∘ layout. Several experiments were conducted under three mode mixities φ=0.15, 0.35 and 0.65 as well as pure modes I (φ=0) and II (φ=1.0) following the established standard procedures. Energy release rates were calculated using an appropriate reduced form of the J integral. Fracture toughness was independent of the interface at initiation but increased with mode mixity. Subsequent fracture resistance was negligible for the 0∘//0∘ layout, but increased significantly for the +45∘//−45∘ interface. Mechanistic investigations were carried out using X-ray computer tomography at 5 different load levels as well as transverse cross sections. The results showed lack of bridging in the case of 0∘//0∘ layout for all values of φ. For the +45∘//−45∘ interface, fracture was dominated by delamination, ply splitting and crack migration with their extent dependent upon φ. Numerical analyses based on the virtual crack closure technique demonstrated that the antisymmetric local fracture modes, interlaminar longitudinal shear vs. transverse shear, are responsible for delamination and crack migration, respectively. Based on the experimental observations, a mesoscale FE model was able to reproduce not only the failure mechanisms, i.e. delamination, transverse cracking and crack migration resulting in the zig-zag fracture pattern, but also give a reasonable approximation of the energy release rate obtained for each of the different mode mixities considered in this study.

Plastic stress intensity factor behavior at small and large scale yielding

In this paper the plastic stress intensity factor (SIF) is used to study the coupling effects of loading biaxiality, material properties and cracked body configuration in both the small- and large-scale yielding ranges. A finite element (FE) analysis is performed for a cracked Mode I plane strain plate subjected to biaxial tension/compression loading. The governing parameter of the elastic–plastic crack-tip stress field In factor at the crack tip, J-integral, and the plastic SIF, are calculated as a functions of loading biaxiality and applied stress levels. Special emphasis is put on the behavior of J-integral and the plastic SIF for specified test specimen geometries under mixed mode loading. Finally, the applicability of the plastic SIF approach to large-scale yielding analysis is also discussed.

Numerical simulation of delamination growth in fiber reinforced polymer laminates using cohesive zone modeling

In this study, the key parameters of cohesive zone modeling, which significantly affect the accuracy in delamination problems, are examined. The study is performed on various standard fracture toughness specimens subjected to mode I, mode II and mixed mode loading. The compressive buckling of a composite laminate is then modeled and the results are validated using virtual crack closure technique. It is shown that the bi-linear interface law with identified parameters provides the best match for the standard fracture toughness specimens while for buckling delamination the effect of interface law shape and interfacial strength is substantial and cannot be ignored.

Micromechanical investigation of snow failure under mixed-mode loading

An intimate understanding of snow failure, particularly under mixed-mode shear and normal loading, is a key ingredient for numerical modelling of snow avalanche release. Due to its highly porous structure, the failure of snow can result in a volumetric collapse. Despite its importance, snow failure and collapse remain poorly understood, mainly due to the fragile nature of the material, which renders systematic experimental exploration difficult and complicates observation at the microscopic level. A microstructure-based discrete element model of snow has been developed and utilized to study snow failure under mixed-mode loading. Depending on applied normal stress, three distinct failure regimes are identified, characterized by different volumetric responses. Shear-induced macroscopic collapse is observed to develop above a critical level of normal stress. A deeper understanding of the mechanisms leading to this volumetric collapse is investigated on the microscopic scale. Force chain buckling within the snow sample leads to volumetric collapse, while stable force chains result in a localized failure and the absence of a volumetric collapse. The stability of the force chains is shown to be insured by the grain contacts between the force chains and the surrounding material. The ratio of contacts close to failure is identified to control the absence or presence of collapse after failure.

Mixed mode fracture characterization of brittle and semi-brittle adhesives using the SCB specimen

Fracture mechanics and damage mechanics are widely used to predict the mechanical behavior of adhesive joints. The critical energy release rate is one of the most important parameters in these models. In practice, most adhesive joints experience mixed mode loading conditions. Therefore, mixed mode fracture energy measurement plays an important role in adhesive joint failure analysis. A new test method for mixed mode fracture energy measurement of brittle and semi-brittle adhesive joints is presented in this paper using semi-circular bend specimens. A data reduction scheme based on a finite element analysis is suggested and finite element results are validated by digital image correlation strain measurement technique. The fracture envelops obtained from the proposed specimen are compared to double cantilever beam (DCB), single leg bending (SLB) and, end-notched flexure (ENF) test results. Good agreement between the new specimen and the classic energy measurement methods is observed.

On the improvement of analytical delamination model for drilling of laminated composites using Galerkin method

Despite the fact that fiber reinforced polymer composite laminates have high strength to density ratio, they have machinability limitations. Drilling operation is one of the mostly used machining processes on the laminated composites as it plays a significant role on assembly of composite parts. The most critical damage, affecting drilled composites, is delamination. Using Galerkin method, this paper, proposes a new model, removing most of the assumptions of previous models. The result of this study can be used to precisely and more reliably predict the critical thrust force-feed rate at which delamination could occur. The model uses the results of cutting theory to predict the distribution of the drilling load on delaminated area, a modified variety of Mindlin–Reissner plate theory in conjunction with the linear elastic fracture mechanic theory in mixed mode loading condition for the prediction of critical thrust force. Comparing with the previous proposed models, it has no assumptions for the load distribution and it considers mode I and mode II simultaneously for the growth of the delaminated zone, which makes it possible to consider non-uniform loading conditions of the drilling process. Using this model, the effect of the distribution of the drill force on the composite is investigated. The critical thrust force was studied for load-controlled and displacement-controlled loading conditions. For the experimental validation, the onset of the growth of the crack was detected using acoustic emission. The results of the experiment were compared with that of model.

In-phase and out-of-phase mixed mode loading: Investigation of fatigue crack growth in SEN specimen due to tension–compression and torsional loading

Numerous cases of damage by fatigue in structures are related to mechanical stresses due to mixed mode loading conditions. To prevent such cases of failure a precise knowledge of the corresponding theoretical background is indispensable. Unfortunately, it is not yet possible to satisfactorily describe the crack propagation by considering a superposition of all three crack modes. For this purpose, experiments on single-edge notched specimens made of 34CrNiMo6 under tension-torsion with different mixed mode ratios and phase shift angles were performed. The focus of the investigations is especially on the kinking and the twisting angle of the crack as well as on the influence on the residual lifetime. Furthermore, existing concepts concerning the prediction of the crack growth under mixed mode are evaluated.

Crack kinking in isotropic and orthotropic micropolar peridynamic solids

A micropolar peridynamic model is presented for characterizing crack propagation in isotropic and orthotropic brittle materials. The analytical formulation of the two-dimensional model is based on the definition of a micropotential energy function that accounts for the four independent elastic constants that define orthotropy and that in the limit can be reduced to isotropy. A distinctive feature of the model is that the bonds’ elastic parameters are continuous functions of orientation with respect to principal material axes. By defining three deformation parameters that quantify bond stretch, bond shear deformation and particles relative rotation, the first continuum bond-based peridynamic model is obtained for two-dimensional Cauchy orthotropic materials characterized by four independent material moduli that is suitable for describing fracture as well as homogeneous and non-homogeneous deformations.The accuracy of the computational model as applied to crack-tip analyses is assessed by comparing the displacement and stress fields within the boundary layer that develops in the immediate vicinity of a crack with the analytical asymptotic results for an orthotropic continuum. The extension of such cracks when they are subjected to mixed-mode loading is simulated under the assumption of illustrative crack extension criteria, and the predictions are compared to those of the maximum hoop stress intensity factor criterion (HSIF-criterion) and the maximum energy release rate criterion (G-criterion).

A concept for defining the mixed-mode behaviour of tough epoxy film adhesives by single specimen design

Fracture modes I and II interact in mixed-mode loading conditions, and the interaction is typically taken into account using a mixed-mode fracture criterion. In this work, a concept for defining the criterion is developed through an experimental-numerical simulation analysis. The mixed-mode behaviour for the criterion is tested and analysed with a single specimen design. The design of the specimen simplifies the measurement when complex test arrangements and preparations for various specimen geometries are excluded in practice. Here, the mixed-mode fracture behaviour of the specimen is analysed in detail using digital image correlation (DIC). The DIC data are used in collaboration with a finite element–based crack onset analysis, including the virtual crack closure technique, in order to consider the typical simplifications and their effects on the mixed-mode criterion. As a benchmark case, the fracture criterion is determined for an epoxy film adhesive FM 300-2 using the developed approach. The developed approach was shown to be feasible and effective for defining the mixed-mode fracture criterion. The determined Power law criterion’s exponents were below unity, which points out that the common (presumed) exponent values in the current literature are actually unconservative.

Experimental and theoretical fracture assessment of rock-type U-notched specimens under mixed mode I/II loading

The aim of this paper is to present a new approach for predicting the mixed-mode fracture resistance of rock-type specimens containing U-shaped notches. The new approach is a modified form of maximum tangential stress (MTS) criterion which states the fracture takes place when the maximum tangential stress at the critical distance from the notch border attains critical value. The critical distance in rock-type specimen is relatively large and the formulations presented in the conventional MTS for characterizing the tangential stress component cannot provide good estimates. Therefore, the modified MTS (MTS-FEM) criterion proposes that the value of maximum tangential stress at the critical distance is determined directly from finite element analysis. Several mixed-mode fracture tests were conducted on the Brazilian disks weakened by central U notches in order to evaluate the MTS-FEM criterion. The comparison between the fracture loads obtained from experiments and those predicted by the MTS-FEM criterion shows that the MTS-FEM criterion can provide good estimates for fracture loads of rock-type U-notched samples under mixed mode loading.

Investigation into the fracture mechanism and thermal conductivity of borophene nanofilm; a reactive molecular dynamics simulation

In the present work, we carry out reactive molecular dynamics simulations to investigate the fracture and thermal behavior of borophene nanofilms. First, we focus on mode I fracture of polycrystalline models with different grain sizes and study the crack propagation behavior of polycrystalline borophene sheets with various initial edge crack sizes under mixed-mode loading. The effect of the misorientation angle of each lattice on the crack propagation was also considered. We find that the single primary crack bifurcates into two or more branches under mixed-mode loading conditions when the speed of the crack exceed a certain level. This tendency is independent of the initial crack size and the strain rates. Secondly, we take advantage of equilibrium molecular dynamics (EMD) to study the thermal behavior of pristine borophene and predict a thermal conductivity of pristine borophene with honeycomb atomic pattern of 35 ± 10 Wm-1K-1.

Ductile and brittle crack-tip response in equimolar refractory high-entropy alloys

Understanding the strengthening and deformation mechanisms in refractory high-entropy alloys (HEAs), proposed as new high-temperature material, is required for improving their typically insufficient room-temperature ductility. Here, density-functional theory simulations and a continuum mechanics analysis were conducted to systematically investigate the competition between cleavage decohesion and dislocation emission from a crack tip in the body-centered cubic refractory HEAs HfNbTiZr, MoNbTaVW, MoNbTaW, MoNbTiV, and NbTiVZr. This crack-tip competition is evaluated for tensile loading and a totality of 15 crack configurations and slip systems. Our results predict that dislocation plasticity at the crack tip is generally unfavorable – although the competition is close for some crack orientations, suggesting intrinsic brittleness and low crack-tip fracture toughness in these five HEAs at zero temperature. Fluctuations in local alloy composition, investigated for HfNbTiZr, can locally reduce the resistance to dislocation emission for a slip system relative to the configuration average of that slip system, but do not change the dominant crack-tip response. In the case of single-crystal MoNbTaW, where an experimental, room-temperature fracture-toughness value is available for a crack on a {100} plane, theoretical and experimental results agree favorably. Factors that may limit the agreement are discussed. We survey the effect of material anisotropy on preferred crack tip orientations, which are found to be alloy specific. Mixed-mode loadings are found to shift the competition in favor of cleavage or dislocation nucleation, depending on crack configuration and amplified by the effect of material anisotropy on crack tip stresses.

A 3D benchmark problem for crack propagation in brittle fracture

We propose a full 3D benchmark problem for brittle fracture based on experiments as well as a validation in the context of phase-field models. The example consists of a series of four-point bending tests on graphite specimens with sharp V-notches at different inclination angles. This simple setup leads to a mixed mode (I + II + III) loading which results in complex yet stably reproducible crack surfaces. The proposed problem is well suited for benchmarking numerical methods for brittle fracture and allows for a quantitative comparison of failure loads and propagation paths as well as initiation angles and the fracture surface. For evaluation of the crack surfaces image-based 3D models of the fractured specimen are provided along with experimental and numerical results. In addition, measured failure loads and computed load–displacement curves are given. To demonstrate the applicability of the benchmark problem, we show that for a phase-field model based on the Finite Cell Method and multi-level hp-refinement the complex crack surface as well as the failure loads can be well reproduced.

Influence of interface crack and non-uniform cement thickness on mixed-mode stress intensity factor and prediction of interface failure of cemented acetabular cup

The goal is to determine the influence of interface crack and non-uniform cement thickness on mixed-mode stress intensity factors (SIF) and the prediction of interface failure of the cemented cup. Nine three-dimensional (3D) finite element (FE) models of implanted pelvic bone were developed having the uniform and non-uniform cement thickness based on computed tomography (CT) dataset. Physiological loading conditions and location-dependent material properties of cancellous bone were considered for the present analysis. In order to understand the influence of crack at cement-bone and implant-cement interfaces, two-dimensional (2D) cracked models were generated and solved using the element free Galerkin method (EFGM). For cracked analysis, a rectangular section was considered at both the interfaces in the superior, inferior, anterior, and posterior anatomic locations to determine the SIF. The average stress values obtained from 3D FE analysis was transferred at the cut boundary of the rectangular section and considered as a mixed-mode loading condition to understand the influence of crack and non-uniform cement thickness on interface failure. The results of the present study indicated that the cement thickness plays an important role in interface failure. SIF increases as the cement thickness decreases. Anterior location is more prone to failure as compared to other anatomic locations. The chance of cement-bone interface failure is more as compared to the implant-cement interface. The present study also indicated that the chance of interface failure is more for the generation of edge crack as compared to center crack.

Mode II crack shielding in a compressed rough crack with friction

In this paper, a two-dimensional model to describe the non-planar geometrical features of crack morphologies is presented. The model accounts for frictional tractions along the crack surfaces by considering a rigid-plastic constitutive interface law. Dilatancy effect due to crack roughness is described by the model, leading to a Mode I/II coupling between displacements and tractions along the crack surfaces. The non-linear solution of the rough and frictional crack under general remote loading paths is obtained using the Distributed Dislocation Technique (DDT). By considering a linear piecewise periodic profile of the interface crack, the influence of roughness and friction of an edge crack is examined in relation to both the resulting near-tip stress field and the fracture resistance under monotonic mixed-mode loading. The present model is capable of quantifying the increase of the fracture resistance due to roughness- and friction-induced crack tip shielding.

Averaged strain energy density estimated rapidly from nodal displacements by coarse FE analyses: Cracks under mixed mode loadings

AbstractThe strain energy density (SED) averaged over a structural volume allows to assess the fracture and fatigue behaviour of cracked components under mixed‐mode loadings. To rapidly estimate the averaged SED, two approaches have been previously proposed: (a) the direct approach; (b) the peak stress method (PSM) and nodal stress (NS) approach. In this paper, the nodal displacement (ND) approach is presented to rapidly estimate the averaged SED from the nodal displacements by FE analyses. This method combines the advantages of all previous approaches, ie, the use of coarse meshes able to capture the contributions of both stress intensity factors (SIFs) and higher order terms, without requiring geometrical modelling of the control volume. To validate the method, cracked plates and cracked bars under mixed‐mode loadings have been analysed. The averaged SED values estimated by the ND approach agree with those calculated by the direct approach, within a range of applicability.