Compact Tension Shear Specimen Research Articles

Mixed-mode crack growth analysis using a cyclic plasticity model

The effects of two singularity fields, namely, the HRR solution and modified form of the nonlinear kinematic hardening (NKH) solution, on the pure mode I and mixed mode I/II fatigue crack propagation were investigated. Experiments and computations were performed on compact tension shear (CTS) specimens of P2M steel, aluminium 7050, and Ti-6Al-4V with different monotonic and cyclic elastic–plastic properties. The analysis of the experimental data on the crack growth rate for all tested materials is given in terms of plastic stress intensity factors (SIFs) according to the HRR and NKH models. The elastic–plastic crack tip fields were obtained by FE computation as a function of the position along the curvilinear crack path for the monotonic condition and the first several cycles of fatigue deformation considering the Bauschinger effect. As a complement to the FE modelling, digital image correlation (DIC) measurements of the displacement and strain fields around the crack tip in the CTS specimens were performed. This study aimed to obtain more detailed information on the local cyclic strain ahead of the mixed mode crack tip by using DIC. From the sensitivity analysis, it was established that the DIC value depended significantly on the location along the crack direction of the pair of points selected before and behind the crack tip. In this study, acceleration or retardation of the crack growth rate in terms of the NKH plastic SIF with respect to the HRR model was observed because of the coupling effect of the mode mixity and cyclic plastic properties of the tested P2M steel, aluminium 7050, and Ti-6Al-4V.

Integral-based non-local approach to ductile damage and mixed-mode fracture

The present study focuses on the application of an integral-based approach for constructing non-local ductile damage models. The incorporation of non-locality into the damage accumulation rule enhances the modeling framework and yields simulation results that are physically reasonable, avoiding the issue of pathological mesh-dependence. To achieve a precise depiction of damage accumulation and fracture under mixed-mode I/II loading, novel delocalization kernels are proposed. These kernels explicitly consider the heterogeneity of stresses and strains in the fracture process zone; the new kernels are categorized into stress-based and strain-based families. Furthermore, rigorous receiver-based normalization procedures and physically meaningful source-based normalizations are explored for the developed kernels. The outcome of this study is the modeling tool, suitable for end-to-end simulations of damage accumulation and fracture. Using a well-calibrated material model, the practical applicability of the new approach is demonstrated by performing finite element analysis on fracture tests conducted on compact tension–shear specimens. In contrast to the conventional delocalization kernels, the newly introduced families of kernels offer an additional fitting parameter, valuable in accurately describing the structural behavior under mixed-mode loading conditions. In particular, the proposed approach enables control over the shape of the predicted KIc–KIIc diagram.

Fatigue Crack Growth Studies under Mixed-Mode Loading in AISI 316 Stainless Steel

The objective of this study is to examine the behavior of fatigue crack growth (FCG) in the mixed mode (I/II) of the AISI 316 austenitic stainless steel alloy, considering mode mixity angles of 30°, 45°, and 60°. This particular alloy is widely used in the marine industry and various structural components because of its exceptional properties, such as high corrosion resistance, good formability, weldability, and high-temperature strength. By investigating the crack growth behavior, the study seeks to provide insights into the material’s durability and potential for long-term use in demanding applications. To analyze fatigue crack growth behavior using linear elastic fracture mechanics (LEFM), this study utilizes compact tension shear (CTS) specimens with varying loading angles. The CTS specimens provide an accurate simulation of real-world loading conditions by allowing for the application of various loading configurations, resulting in mixed-mode loading. The ANSYS Mechanical APDL 19.2 software, which includes advanced features such as separating, morphing, and adaptive remeshing technologies (SMART), was utilized in this study to precisely model the path of crack propagation, evaluate the associated fatigue life, and determine stress intensity factors. Through comparison with experimental data, it was confirmed that the loading angle had a significant impact on both the fatigue crack growth paths and the fatigue life cycles. The stress-intensity factor predictions from numerical models were compared to analytical data. Interestingly, it was observed that the maximum shear stress and von Mises stresses occurred when the loading angle was 45 degrees, which is considered a pure shear loading condition. The comparison shows consistent results, indicating that the simulation accurately captures the behavior of the AISI 316 austenitic stainless steel alloy under mixed-mode loading conditions.

Analysis of mixed-mode Compact-Tension-Shear (CTS) specimens with slanted propagating cracks

Compact-Tension-Shear (CTS) specimen with its loading device has been widely used in mixed-mode I&II fatigue crack growth (FCG) experiments. To accurately describe the FCG behavior of materials, it is necessary to determine both the crack length and the parameters that represent crack driving force or crack front stress field in real-time. However, the relevant solutions are currently incomplete or insufficient. In this paper, for CTS specimen with slanted propagating crack, the variations of stress field parameters including stress intensity factors (SIFs) and T-stresses, as well as crack-mouth-opening-displacement (CMOD) compliance were investigated through finite element (FE) analysis. The results show that KI, KII and T11 are greatly influenced by the initial crack length ratio, the slanted propagating crack length ratio and the loading angle, but rarely by the specimen thickness among the considered range of geometries; T33 as an out-of-plane constraint parameter, however, is subject to the coupling effects of in-plane geometries, out-of-plane geometries and the mixed-mode loading. Moreover, it is shown that the measurement span has an effect on CMOD-compliance results for CTS specimens under mixed-mode loading, which is only negligible within the recommended range of D/W∈(0.02, 0.16]. Finally, the accuracy of the developed CMOD-compliance equations was validated through FCG experiments. The conclusions obtained in the current work will provide usable constraint-related crack front stress field parameter solutions for the analysis of FCG behavior in mixed fracture mode, and also give a reliable non-visual method for the determination of fatigue propagating crack length in CTS experiments.

Scaled fatigue cracks under service loads

Scaled experimentation is a powerful engineering tool yet its application to fatigue is limited by significant changes in behaviour with scale. The recent discovery of new similitude rules however opens new possibilities that are explored in this work through numerical experimentation for industrially representative fatigue-crack growth scenarios. It is shown for the first time, how the geometric size effects present in mixed mode fatigue tests are eliminated by performing two appropriately designed scaled experiments. The first order finite similitude theory is applied to mixed mode (modes I and II) fatigue crack growth in three case studies, viz., compact tension shear (CTS) specimen, wing fuselage attachment lug, and a T-joint with an inclined semi elliptical crack. Both planar and non-planar crack growth feature, along with surface and through thickness cracks. Low and high cycle fatigue (up to circa 60,000 cycles) is examined for three different materials (Al-6061 T6 alloy, structural steel, and AISI 316 stainless steel) under a variety of load ratios. The new rules return near exact crack-path predictions whereas lifecycle predictions have errors ranging between 1 % and 9 %. Paris law constants C and m are predicted with up to 99.9 % accuracy supporting the theory that Paris law is a first order similitude rule. Geometric size effects afflicting industrial type scaled-fatigue studies employing a damage tolerant design approach are confirmed to be eliminated on combination of information from two appropriately designed scaled models.

Analysis of stop-hole effects on mode I-II fatigue crack behavior for Q420 steel using experiments, FEM and variable length RNN approaches

To investigate the stop-hole effect on the fatigue crack path and life under mixed I-II cyclic loads, the compact tension-shear specimens with different stop-hole diameters were adopted to perform a series of tests under various loading angles. The results show that the fatigue life increases with the loading angle, and also increases with the hole diameter. Numerical simulation was used to enhance the experimental database. Based on the database, a variable-length recurrent neural network is proposed which memories the crack segment information at previous learning step. The results are encouraging and provide an inspiration to evaluate the safety of components.

Experimental and numerical investigation of mixed-mode fatigue crack growth in nickel-based superalloy at high temperature

Fatigue cracking is one of the most common damage modes of aeroengine hot-end components, usually subjected to mixed-mode cracking. In this study, mixed-mode fatigue crack growth experiments at 550 °C are carried out using compact tension shear specimens made of nickel-based superalloy GH4169. Adaptive finite element method was used to verify several models at high temperature. The accuracy of angle dependent models was higher at 550 °C, and the rate of da/dN increased and decreased twice with crack propagating, which is different from room temperature (20–25 °C). This research could provide a basis for lifespan prediction of aeroengine hot-end components.

Crack initiation characteristics of brittle materials with I‐II mixed mode crack under uniaxial compression

AbstractConsidering T‐stress components under compression, the crack initiation characteristics of HT200 and PMMA under uniaxial compression have been investigated by theoretical analysis and experimental study for central cracked plate (CCP) and compact tension shear (CTS) specimens with I‐II mixed mode crack. Crack initiation angles of CCP and CTS specimens under compressive load were theoretical predicted according to modified maximum tangential stress (MMTS) criterion and modified maximum shear stress (MMSS) criterion. The influence of material parameters and specimen geometrical configurations on crack initiation characteristics was illustrated through experiments. It demonstrates that the modified fracture criterion considering T‐stress components is more consistent with experiments. Crack initiation angle is related to material properties. Limit load PL is controlled by KII under compression for CCP specimen, and PL of PMMA is less than that of HT200. The closure effect on CTS specimens is less significant than that on CCP specimens.

Numerical and experimental investigation of mixed‐mode crack growth in aluminum alloys

AbstractFatigue crack growth in Al 2024 and Al 7050 specimens was assessed experimentally and numerically. In the experimental investigation, various specimen configurations and loading conditions were used to achieve pure mode I, pure mode II, and mixed mode I/II, I/III, and I/II/III. Sample configurations were as follows: first, compact tension shear (CTS) specimen to reproduce pure mode‐I and pure initial mode‐II loading conditions; second, surface crack tension (SCT) specimen to analyze the behavior of semielliptical surface cracks in mode‐I and mixed‐mode conditions; and third, hollow cylindrical (HC) specimen with initial semielliptical surface crack to analyze fatigue crack growth under complex stress state. In the numerical study, finite element method (FEM) simulations were performed by means of FRANC3D and ABAQUS solver. The numerical predictions were validated with the experimental results. These predictions resulted to be accurate estimation of the crack growth across the broad range of the investigated loading conditions.

Windows to trigger crack branching for cracked solids under mixed Mode-I/II loading

For a cracked solid under mixed Mode-I/II loading, the present investigation shows that six energy-based driving forces act respectively on the six subintervals around a crack tip, which controls the underlying fracture configurations, including complex crack branching. Using the geometrical modelling that describes multiple cracks initiation from a crack tip and a mixity parameter φn, subinterval division for crack tip boundary to maximized the energy release rate has been proposed. This is an efficient way to reveal theoretically energy-based driving forces acting on the local boundaries around a crack tip, and to show that the number of the subintervals is no greater than six. Three windows are suggested, within which the crack multiple-branching is more likely to be triggered. Compact tension shear (CTS) specimens made from general-purpose Polystyrenes (GPPS) under mixed Mode-I/II loading for a given φn are considered to investigate fracture behaviors. The typical experimental findings are consistent with some typical fracture behaviors predicted by the present modelling. The current theoretical and experimental investigations could be helpful to refresh the understanding of crack branching under quasi-static or dynamic mixed Mode-I/II loading.

Inversion of dislocation densities under mixed mode fracture

Mixed-mode crack growth is here investigated through experiments and computations for 34X and P2M steels, 7050 aluminium, and Ti-6Al-4V alloys in a compact tension shear (CTS) specimen. In this study, we use the mechanism-based strain gradient (MSG) plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on local stress distributions. The constitutive relations are based on Taylor’s dislocation model, which allows to gain insights into the role of the increased dislocation density associated with large gradients in plastic strain near cracks. The material model is implemented in a commercial finite element (FE) software package using a user subroutine, and the nonlinear stress intensity factors (SIFs) are evaluated as a function of the intrinsic material length. As a result of the FE calculations of dislocation density distributions, the effects of both the fracture mode and the stress–strain state are determined. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. Dislocation densities, stress fields and nonlinear SIF solutions are determined for experimental curvilinear crack paths by taking into account the transition from the initial Mode II crack to the mixed-mode fracture.

Fatigue crack growth under mixed mode I + II in Ti-6Al-4V specimens produced by Laser powder Bed fusion

Mode I and mode I + II fatigue crack growth experiments are performed using compact tension shear specimens made of Ti-6Al-4V by additive manufacturing for various loading angles. The performance of various methodologies used to determine the equivalent stress intensity factor were studied, obtaining good results in simpler methods when the crack deflection angle was also included in the algorithm. The crack growth speed didn’t suffer significant alterations due to similar values of crack deflection angle, mode I loading predomination and similar crack closure effect. Fractured surfaces presented irregular regions consequence of intergranular separation between α phase and agglomerations of β phase.

Mixed mode crack paths in terms of plastic stress intensity factors based on conventional and strain gradient plasticity

The effect of an initial mode II loading on subsequent mixed-mode crack path was investigated through experiments and computations for 34X and P2M steels, 7050 aluminum, and Ti-6Al-4V alloys in a compact tension shear (CTS) specimen. An optical microscope and the drop potential method were used to determine the actual position of the crack tip on the curvilinear crack path monitoring and continuous measurements of the crack size were made along the path in the CTS specimen. In accordance with these experimental observations, the main feature of the initial mode II fracture is the crack growth on a curvilinear path. For subsequent mixed-mode crack propagation, the crack front continuously changes the shape and direction with each loading cycle. For a mode II loaded initial crack, the scenario becomes more complex because of the change in the propagation direction when a kinked crack is formed. The experimental data on crack growth for all tested materials are represented in terms of the elastic and new plastic stress intensity factors (SIFs). To this end, both the classical and the conventional mechanism-based strain-gradient plasticity (CMSGP) theories were employed. The material constitutive equation is implemented in a finite element code and the elastic and plastic fracture resistance parameters are calculated as a function of the position along the curvilinear crack path in all tested CTS specimens produced from 34X and P2M steels, 7050 aluminum and Ti-6Al-4V alloys. As a result of the finite element calculations, nonlinear amplitude factor solutions are determined across a wide range of material work hardening conditions, and the role of the Taylor’s intrinsic material length and both the coupled effect of these parameters are established. The potential of fundamental and practical applications of introduced fracture resistance parameters are discussed.

Couple analysis of DIC and FEM to quantify strain fields and crack-flank displacements in structural materials under cyclic mixed-mode I/II fracture

Mixed mode cyclic fracture under multiaxial stress-strain state is critical for the generation of appropriate damage tolerance methodologies. To this end the elaborated approach is dedicated to full range of mixed mode loading for elastic-plastic plane problem. In this study, the digital image correlation (DIC) experimental results are represented as contours as well as radial strain distributions in the local system of coordinate centered at the current crack tip position along curvilinear crack path. As a complement to the DIC measurement, finite element (FE) modelling of the displacement and strain fields around the crack tip in the compact tension shear (CTS) specimen was performed in order to reproduce experimental mixed mode loading conditions. In this study, for comparison aim we used the conventional mechanism-based strain gradient (CMSG) and classical Hutchinson–Rice–Rosengren (HRR) plasticity theories to evaluate the coupled effect of the material plastic properties and the mode mixity on the crack tip behaviour. The new material model is implemented in a commercial finite element software package ANSYS 2021R1 using a user subroutine. The intention with this work was to complement the DIC measurements as well as acquire more detailed information about the local strain ahead of the crack tip and the crack opening. From a sensitivity analysis it has been established that the DIC value depends significantly from the location along the crack direction of the pair of points selected before and behind the crack tip. As a result of the FE calculations of strain distributions, the effects of both the fracture mode and the material properties are determined.

Three-Dimensional analysis of mixed mode Compact-Tension-Shear (CTS) Specimens: Stress intensity Factors, T-stresses and crack initiation angles

In order to characterize the crack tip stress field in three-dimensional fatigue and fracture problems, stress intensity factor and T-stress solutions are usually necessary. In this paper, extensive three-dimensional (3D) finite element models are constructed for Compact-Tension-Shear (CTS) specimen, which is one of the most widely used specimens for fatigue and fracture tests under mixed-mode I&II loading. In-plane and out-of-plane geometric dimensions including varying crack depths ratios (a/W = 0.3, 0.5 and 0.7) and thicknesses ratios (B/W = 0.1, 0.3 and 0.5) are considered under different loading angles (β = 0°, 15°, 30°, 45°, 60°, 75° and 90°). The results of stress intensity factors (KI,KII and KIII) and T-stresses (T11 and T33) along the crack front are computed and analyzed. The combined effects of geometric dimensions and loading angles on these fracture parameters have been illustrated. The solutions of the parameters are then described using empirical formulae by fitting numerical results with the least-squares method. Solutions obtained have been used to predict the crack initiation angles for CTS specimens based on mixed-mode fracture criteria including the maximum tangential stress (MTS) criterion, the generalized MTS (GMTS) criterion, the strain energy density (SED) criterion and the generalized SED (GSED) criterion. Solutions are useful for fracture and fatigue problems of mixed-mode I&II, such as analysis of the constraint effects on fracture toughness and propagation path of fatigue crack.

Fracture resistance characteristics of mild steel under mixed mode I-II loading

The fracture resistance of elasto-plastic materials varies significantly depending on the mode mixities, i.e., the loading combinations. This paper aims to experimentally investigate the fracture resistance and behaviour of two grades of mild steel under various in-plane loading combinations. A loading fixture with high loading capacity and modified compact tension shear (CTS) specimen are designed to conduct fracture tests on elasto-plastic materials under various mode mixities. A digital image correlation (DIC) technique-based method is developed and verified to detect the fracture initiation. It is found in the paper that the sensitivity of the fracture resistance of steel to mode mixity is attributed to the strain hardening capacity and the impurities in chemical composition of the steel. It is also found that the plastic strain concentration, crack tip blunting and fracture mechanism lead to different fracture resistance of both types of steel under various mixed mode loading combinations. The contribution of the paper is that an additional method to determine the fracture initiation under non-mode I loading is developed. The test results show the necessity of considering the mode mixity effect under the mode II loading dominance in practical engineering applications.

Fatigue crack growth under mixed-mode I + II and I + III in heat treated 42CrMo4 steel

The paper contains the results of an experimental investigation of fatigue crack development under mixed-mode I + II and I + III in heat-treated 42CrMo4 steel. Tests were performed on heat-treated compact tension shear specimens and rectangular cross-section specimens for mixed-mode I + III. Mixed-mode I + II tests were conducted for 30 and 60° loading angle, while the test for I + III mixed-mode was conducted for 30 and 45°. Additionally, the paper presents fracture analysis results of fatigue crack path development.

Experimental Evaluation on Mixed Mode I/II Stress Intensity Factors using CTS welded and non-welded specimen of Aluminum Alloy AA3003

In the present paper, experimental investigation on the fracture of aluminum alloy AA3003 are conducted on the Compact Tension Shear CTS specimen non-welded and CTS specimen welded by FSW process under mixed mode loading by using Arcan loading device based on Richard’s principle suitable for mixed mode. All loading in mixed mode starting from pure tension (mode I) up to pure shear (mode II) can be obtained and tested by varying the loading angles from 0° to 90°. The stress intensity factor for the Compact Tension Shear (CTS) specimen are determined three normalized lengths cracks 0.3, 0.5 and 0.7.The length of notches influence on the variation of stress intensity factor KI, KII. For CTS specimen with notches with a short length, the values of KII are greater than those obtained for notches with a long length.

Computational Simulation of 3D Fatigue Crack Growth under Mixed-Mode Loading

The purpose of this research was to present a simulation modelling of a crack propagation trajectory in linear elastic material subjected to mixed-mode loadings and investigate the effects of the existence of a hole and geometrical thickness on fatigue crack growth and fatigue life under constant amplitude loading. For various geometry thickness, mixed-mode (I/II) fatigue crack growth studies were carried out to utilize a single edge cracked plate with three holes and compact tension shear specimens with various loading angles. Smart Crack Growth Technology, a new feature in ANSYS, was used in ANSYS Mechanical APDL 19.2 to predict the cracks’ propagation trajectory and their consequent fatigue life associated with evaluating the stress intensity factors. The maximum circumferential stress criterion is implemented as a direction criterion under linear elastic fracture mechanics (LEFM). According to the hole position, the results demonstrate that the fatigue crack grows towards the hole due to the unbalanced stresses on the hole induced crack tip. The results of this simulation are verified in terms of crack growth paths, stress intensity factors, and fatigue life under mixed-mode load conditions, with several crack growth studies published in the literature showing consistent results.

A CA-XFEM for mixed-mode variable-amplitude fatigue crack growth

In this research, the extended finite element method (XFEM) in conjunction with the combined approximation (CA) is utilized for estimating the fatigue life of two-dimensional isotropic bodies under variable-amplitude loading. In the proposed method, called CA-XFEM, in addition to the fact that no re-meshing process is required, the crack growth path is determined without the need to solve the whole system of equations which these features significantly reduce computational costs. The Willenborg model is employed for modeling the retardation effect due to the overloads in the load history. For validation of the method, the numerical results are compared with the existing experimental data for a compact tension specimen made of Al 7075-T6 and a compact tension shear specimen made of Al 5083-H111. It is observed that the developed CA-XFEM Matlab code has excellent capability in modeling variable-amplitude fatigue crack propagation considering the retardation effect. Also, the effect of ratio and sequence of overload and mixed-mode overloading on the fatigue crack growth are studied.