Center-cracked Specimens Research Articles

Should the translaminar fracture toughness of laminated composites be represented by the [formula omitted] or the [formula omitted] curve? A comparison of their consistency and predictive capability

The translaminar fracture toughness of laminated composites can be determined experimentally assuming either linear elastic fracture mechanics (LEFM) or cohesive zone model (CZM) hypotheses. Each theoretical frame is different in terms of complexity and predictive capabilities. To clarify the latter point, we derived the R(Δa) (LEFM) and J(ω) (CZM) curves from a set of published results on over-height compact tension fracture specimens of different sizes. Then, these curves were used to predict the strength of other coupons of the same material (geometrically similar, scaled, open hole and center cracked specimens). Since the idealization of the fracture phenomena in cohesive zone models is more realistic than in LEFM, the fracture property so obtained is more independent from the size of the specimen used to measure it and its predictive capability embraces a wider range of sizes and geometries.

Cyclic Relaxation, Impact Properties and Fracture Toughness of Carbon and Glass Fiber Reinforced Composite Laminates.

In this paper, the mechanical properties of fiber-reinforced epoxy laminates are experimentally tested. The relaxation behavior of carbon and glass fiber composite laminates is investigated at room temperature. In addition, the impact strength under drop-weight loading is measured. The hand lay-up technique is used to fabricate composite laminates with woven 8-ply carbon and glass fiber reinforced epoxy. Tensile tests, cyclic relaxation tests and drop weight impacts are carried out on the carbon and glass fiber-reinforced epoxy laminates. The surface release energy GIC and the related fracture toughness KIC are important characteristic properties and are therefore measured experimentally using a standard test on centre-cracked specimens. The results show that carbon fiber-reinforced epoxy laminates with high tensile strength give high cyclic relaxation performance, better than the specimens with glass fiber composite laminates. This is due to the higher strength and stiffness of carbon fiber-reinforced epoxy with 600 MPa compared to glass fiber-reinforced epoxy with 200 MPa. While glass fibers show better impact behavior than carbon fibers at impact energies between 1.9 and 2.7 J, this is due to the large amount of epoxy resin in the case of glass fiber composite laminates, while the impact behavior is different at impact energies between 2.7 and 3.4 J. The fracture toughness KIC is measured to be 192 and 31 MPa √m and the surface energy GIC is measured to be 540.6 and 31.1 kJ/m2 for carbon and glass fiber-reinforced epoxy laminates, respectively.

Extended finite element simulation on Tensile, fracture toughness and fatigue crack growth behaviour of additively manufactured Ti6Al4V alloy

The mechanical properties such as tensile, fracture toughness, and fatigue properties of Additive Manufacturing (AM) fabricated Ti6Al4V alloy is critically crucial for structural applications. The in-house developed MATLAB-based extended finite elements method (XFEM) model has been utilized to analyse experimental results of fatigue, fracture, and tensile properties of AM fabricated Ti6Al4V alloy, to avoid expensive and destructive mechanical characterisation. The XFEM model was first used to validate the single edge cracked sample of laser powder bed fusion (LPBF) processed Ti6Al4V alloy for fatigue crack growth rate (FCGR). The XFEM simulation study was further extended to analyse fatigue life of center and double-side cracked specimens, as well as for evaluating fracture toughness KIC upon accounting potential crack initiation site. The model has also been developed to predict FCGR of edge cracked specimen under mixed-mode loading conditions. The critical stress intensity factor (SIF) and stress distribution map in the crack vicinity of the C(T) specimen were modelled through FEA Abaqus package to estimate the fracture toughness of Ti alloy. A similar XFEM approach was used to analyse the tensile properties of Ti alloy to predict its fracture behaviour through the center cracked specimen taken at the tensile gauge section. The strengthening mechanisms contributing to Ti alloy's static and dynamic properties are elucidated through microstructural characteristics of LPBF processed Ti6Al4V alloy reported in the literature.

Machine learning-based prediction of the translaminar R-curve of composites from simple tensile test of pre-cracked samples

A novel approach to determine the translaminar crack resistance curve of composite laminates by means of a machine learning model is presented in this paper. The main objective of the proposed method is to extract hidden information of crack resistance from strength values of center-cracked laminates. Compared to traditional measurements, the notable advantage is that only tensile strength values are required which can be obtained by a rather simpler experimental procedure. This is achieved by the incorporation of the finite fracture mechanics, which links crack resistance with strength values. In order to get training dataset, a semi-analytical method using both finite element method and finite fracture mechanics is employed to generate strength values of center-cracked specimens with different random R-curves, which serve as inputs for our artificial neural network. Regarding the outputs, principal component analysis is performed to reduce dimensionality and find suitable descriptors for crack resistance curves. After successfully training machine learning model, experimental studies on basalt fiber reinforced laminates are conducted as validation. Results have proven the effectiveness of the proposed strategy for predicting crack resistance curves, as well as the feasibility of using machine learning-based framework to find out more information about composites from simple experimental data.

Roles of Hydrogen and Plastic Strain Distribution on Delayed Crack Growth in Single-crystalline Fe–Si alloy

Abstract Effects of hydrogen on macroscopic and microscopic features of crack growth in thin specimens were investigated using a thin sheet of single-crystal Fe-3wt%Si alloy. Center-cracked specimens were tested under a sustained load in a hydrogen environment, and under continuous stretching in an air environment. The fracture features were compared to elucidate the role of hydrogen in hydrogen-induced delayed crack growth. In both air and hydrogen environments, the crack growth mode of the thin specimens was the same as that of the thick specimens, despite the significantly reduced thickness. Surprisingly, the crack grew discontinuously, and left striations on the fracture surface, in which shorter striation spacing was observed in hydrogen. In addition, there was a similarity in the deformation microstructures beneath the fracture surface, that is, both microstructures were composed of three distinct layers characterized by different plastic strain gradients and dislocation densities. In the hydrogen environment, the hydrogen-enhanced localized plasticity (HELP) mechanism is believed to be relevant to the crack growth process. Also, HELP was supposed to cause different characteristics (the magnitude of plastic strain, the plastic strain gradient, and dislocation structure) of the three layers in the hydrogen compared to those in the air. Reverse plastic deformation occurred in the regions behind the crack front during crack growth, which is speculated to contribute not only to enlarge the crack tip opening angle (CTOA) but also to blunt the crack tip.

Microscopic examination of striation spacing during ductile crack growth in Fe-3wt%Si single-crystalline thin plates in air and hydrogen

Abstract Microscopic features of crack growth in thin plates of single-crystalline Fe-3wt%Si alloy in both air and hydrogen environments were investigated by electron channeling contrast imaging (ECCI), electron backscattering diffraction (EBSD), as well as scanning electron microscopy fractography. The goal was to elucidate the discontinuous crack growth as well as the constant unit distance of crack extension (striation spacing). Center-cracked specimens were tested under a sustained load in a hydrogen environment, while they were under continuous stretching in the air environment. The following results were obtained. (1) Striation is formed by extensive slips emitted from the crack tip, mainly contributed from specific ( 1 1 ‾ 2 )[ 1 ‾ 11 ] and ( 1 ‾ 12 )[ 1 ‾ 1 1 ‾ ] slip systems. The discontinuous crack growth is mainly caused by interaction of the crack and ( 1 1 ‾ 2 )[ 1 ‾ 11 ] and ( 1 ‾ 12 )[ 1 ‾ 1 1 ‾ ] slip bands/cell walls formed ahead of the crack tip. These slip bands/cells show that the spacing between slip bands/cells is constant and independent of the crack length. Hence, the striation spacing is the same as that of the slip bands/cells ahead of the crack tip. (2) Hydrogen may affect the slip behavior by reducing the spacing between slip bands/cells ahead of the crack tip compared to that in the air environment.

A novel formulation of material nonlinear analysis in structural mechanics

This article demonstrates a novel approach for material nonlinear analysis. This analysis procedure eliminates tedious and lengthy step by step incremental and then iterative procedure adopted classically and gives direct results in the linear as well as in nonlinear range of the material behavior. Use of elastic moduli is eliminated. Instead, stress and strain functions are used as the material input in the analysis procedure. These stress and strain functions are directly derived from the stress-strain behavior of the material by the method of curve fitting. This way, the whole stress-strain diagram is utilized in the analysis which naturally exposes the response of structure when loading is in nonlinear range of the material behavior. It is found that it is an excellent computational procedure adopted so far for material nonlinear analysis which gives very accurate results, easy to adopt and simple in calculations. The method eliminates all types of linearity assumptions in basic derivations of equations and hence, eliminates all types of possibility of errors in the analysis procedure as well. As it is required to know stress distribution in the structural body by proper modelling and structural idealization, the proposed analysis approach can be regarded as stress-based analysis procedure. Basic problems such as uniaxial problem, beam bending, and torsion problems are solved. It is found that approach is very suitable for solving the problems of fracture mechanics. Energy release rate for plate with center crack and double cantilever beam specimen is also evaluated. The approach solves the fracture problem with relative ease in strength of material style calculations. For all problems, results are compared with the classical displacement-based liner theory.

Method of Detecting Unexpected Load Leading to Crack Growth Acceleration

The crack growth can accelerate after applying unexpected overload or underload during usual operation of machine structure. An acceleration or deceleration of the crack growth was observed depending on the experimental conditions. In the present study, a method of detecting the application of an unexpected hazardous load, that is high levels of overload or underload, was investigated. It is expected that the acceleration of crack growth brings catastrophic failure in machine structure. Therefore, it is useful for machine maintenance to know whether an unexpected load was applied or not by doing daily inspection. In the present study by using center-crack specimens, a simple method of detecting application of overload or underload was investigated by using strain information.

Evaluating Fracture Toughness of Rolled Zircaloy-2 at Different Temperatures Using XFEM

Fracture toughness and mechanical properties of the zircaloy-2 processed by rolling at different temperatures have been investigated, and simulations have been performed using extended finite element method (XFEM). The solutionized alloy was rolled at different temperatures for different thickness reductions (25–85%). Fracture toughness has been investigated by compact tension test. The improved fracture toughness of the rolled zircaloy-2 samples is due to high dislocation density. SEM image of the fractured surface shows the reduction in dimple sizes with the increase in dislocation density due to the formation of microvoids as a result of severe strain induced during rolling. Compact tension test, edge crack, center crack and three-point bend specimen simulations have been performed by XFEM. In XFEM, the cracks are not a part of finite element mesh and are modeled by adding enrichment function in the standard finite element displacement approximation. The XFEM results obtained for compact tension test have been found to be in good agreement with the experiment.

Characterization of the translaminar fracture Cohesive Law

Quasi-brittle materials such as fibre-reinforced composite materials develop a relatively large Fracture Process Zone where material toughening mechanisms such as matrix cracking, fibre-bridging and fibre pull-outs take place. The damage onset and damage propagation are well defined from a cohesive model point of view, although no standard procedure has been yet developed to characterize the translaminar Cohesive Law. The present work proposes an objective inverse method for obtaining the Cohesive Law with the use of an analytic model capable of predicting the load–displacement curve of a Compact Tension specimen for any arbitrary Cohesive Law shape. The softening law has been obtained for two laminates, providing an excellent agreement with the experimental results. With the obtained softening function, the nominal strengths of a Center Cracked Specimen and an Open Hole specimen have been predicted for a wide range of specimen sizes.

A comparison of stress in cracked fibrous tissue specimens with varied crack location, loading, and orientation using finite element analysis

Cracks in fibrous soft tissue, such as intervertebral disc annulus fibrosus and knee meniscus, cause pain and compromise joint mechanics. A crack concentrates stress at its tip, making further failure and crack extension (fracture) more likely. Ex vivo mechanical testing is an important tool for studying the loading conditions required for crack extension, but prior work has shown that it is difficult to reproduce crack extension. Most prior work used edge crack specimens in uniaxial tension, with the crack 90° to the edge of the specimen. This configuration does not necessarily represent the loading conditions that cause in vivo crack extension. To find a potentially better choice for experiments aiming to reproduce crack extension, we used finite element analysis to compare, in factorial combination, (1) center crack vs. edge crack location, (2) biaxial vs. uniaxial loading, and (3) crack–fiber angles ranging from 0° to 90°. The simulated material was annulus fibrosus fibrocartilage with a single fiber family. We hypothesized that one of the simulated test cases would produce a stronger stress concentration than the commonly used uniaxially loaded 90° crack–fiber angle edge crack case. Stress concentrations were compared between cases in terms of fiber-parallel stress (representing risk of fiber rupture), fiber-perpendicular stress (representing risk of matrix rupture), and fiber shear stress (representing risk of fiber sliding). Fiber-perpendicular stress and fiber shear stress concentrations were greatest in edge crack specimens (of any crack–fiber angle) and center crack specimens with a 90° crack–fiber angle. However, unless the crack is parallel to the fiber direction, these stress components alone are insufficient to cause crack opening and extension. Fiber-parallel stress concentrations were greatest in center crack specimens with a 45° crack–fiber angle, either biaxially or uniaxially loaded. We therefore recommend that the 45° center crack case be tried in future experiments intended to study crack extension by fiber rupture.

Molecular dynamics simulation-based cohesive zone representation of fatigue crack growth in a single crystal nickel

Nanoscale fatigue crack growth was investigated by introducing a cohesive zone model based on molecular dynamics simulations. The evolutions of the microstructure and stress in fatigue crack growth over two different cyclic loading regimes were investigated using pre-existing centre crack specimens. Under increasing strain amplitude cyclic loading, dislocations emitted and persistent slip bands formed around the fatigue crack tip, which retarded crack propagation and changed the stress distributions; under constant amplitude cyclic loading, crack opening and closing was accompanied by void formation in the crack plane. Different fatigue loading regimes resulted in different crack propagation mechanisms and stress distributions; the peak stress was accompanied by microstructure evolution ahead of the crack tip, which induced the variation in fatigue crack growth rates and crack opening displacements.

Numerical investigation of fracture behavior of nanostructured Cu with bimodal grain size distribution

Nanostructured metals with bimodal grain size distribution, composed of coarse grain (CG) and nanograin (NG) regions, have proved to have high strength and good ductility. Here, numerical investigation, based on the mechanism-based strain gradient plasticity theory and the Johnson–Cook failure model, focuses on effects of (1) distribution characteristics of the CG regions and (2) the constitutive relation of the NG with different grain sizes on fracture behavior in a center-cracked tension specimen of bimodal nanostructured Cu. High strain rate simulations show that both of them directly influence load response and energy history, and importantly, they are closely related to the fracture pattern. This study shows that both CG region bridging and crack deflection toughen the bimodal nanostructured Cu significantly, while debonding enhances the overall ductility moderately. Simulations also show that with volume fraction of the CG regions increasing, both structural strength and ductility of the bimodal nanostructured Cu specimen can be improved.

Effect of stacking sequence and geometric scaling on the brittleness number of glass fiber composite laminate with stress raiser

AbstractThe fracture behavior of quasi-brittle material exhibits commonly brittle behavior with some ductility in the fracture processing zone. Therefore, a matrix of experimental works is performed to investigate the failure behaviors based on a parameter known as brittleness number, which is a measure of brittle behaviors. Glass fiber-reinforced epoxy laminates of three stacking sequences, cross-ply [0/90]2s and two quasi-isotropic [0/45/90]2s and [0/45/90/-45]s, are manufactured using hand lay-up technique. A matrix of different specimen geometric scaling with open hole of the same material is used. The fracture energy GIC and nominal strength of these composite laminates are measured experimentally using compact tension test, center crack specimen, and tension test, respectively. The results showed that the increase of homogeneity of composite laminates, which is introduced by inserting a certain angle ply for the laminate structure, enhanced the material ductility as the brittle number increased. The larger size of specimen leads to the increase of brittleness for the same stacking sequences due to the increase of stress concentration factor.

Analytical model to predict multiaxial laminate fracture toughness from 0° ply fracture toughness

The prediction of nominal strength is very important in the design and evaluation of materials especially polymer matrix composites. Various cohesive laws forms are successfully used in predicting the nominal strength of laminated composite structures. For composite structures, fracture toughness is dominated parameter when using cohesive laws to predict their nominal strength. In spite of complex reported models, this study propose an easy simple model to predict the fracture toughness of multidirectional composite laminates using the fracture toughness of the 0° ply ones. This model is mainly based on the geometry of fiber orientation and linear elastic fracture mechanics and uses the fracture toughness of the 0° ply obtained from compact tension test specimens. A good prediction is obtained by comparing the model results with experimental data which are obtained from center-cracked specimens manufactured using different lay-ups orientations and materials. POLYM. ENG. SCI., 54:234–238, 2014. © 2013 Society of Plastics Engineers

On the relation between the mode I fracture toughness of a composite laminate and that of a 0° ply: Analytical model and experimental validation

This paper proposes a simple model to predict the fracture toughness of multidirectional carbon–epoxy composite laminates using the fracture toughness of the 0° ply. The model is based on a combination of Linear-Elastic Fracture Mechanics and lamination theory, and uses as material properties the ply elastic properties and the fracture toughness of the 0° ply measured in compact tension test specimens. A good correlation is obtained by comparing the model predictions and experimental data obtained in center-cracked specimens manufactured using different lay-ups and materials.

Nonlocal Damage Gradient Model for Fracture Characterization of Aluminum Alloy

This article presents the development of a generalized nonlocal damage-coupled material model. The model introduces the concept of cumulative damage gradient through a set of damage evolution equations within the irreversible thermodynamics framework. The conventional damage-coupled plasticity models require either self-developed finite element codes or the mandatory use of regular elements. The proposed material model is implemented in a commercial finite element code ABAQUS (Version 6.5) via its UMAT subroutine. The implementation of this model on ABAQUS is described with a focus on the nonlocal treatment together with the derivation of the consistent tangent modulus (Jacobian). As a numerical example, the nonlocal damage model is applied to center-cracked specimen made of aluminum alloy 2024-T3. Comparison is made between the computed results and experimental ones. The validity of the proposed model is examined, and its effectiveness for engineering application is elucidated.

Rectangular tensile sheet with a center notch root crack

This paper deals with the rectangular tensile sheet with a center notch crack. Such a crack problem is called a center notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, two center notch models are analyzed in detail. By changing the geometrical forms and parameters of the center notch, and by comparing the SIFs of the center notch crack problem with those of the center cracked plate tension specimen (CCT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the center notch on the stress intensity factors (SIFs) of the center cracked plate tension specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the center cracked plate tension specimen. So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the center cracked plate tension specimen. In addition, the numerical investigation proves that the conventional angular notched specimen is much less sensitive to the size of notch than is the circular notched specimen.

Detection of Crack Growth Rate in 45 Steel by Metal Magnetic Memory

It is important that monitoring the fatigue crack propagation in engineering. This paper studied crack growth rate with the metal magnetic memory technique. Three-point bending fatigue tests of center-cracked specimens were carried out and the normal component of magnetic field signals Hp(y) on the surface of specimens were measure by TSC-1M-4. The correlation of crack growth rate da/dN and metal magnetic memory normal signal Hp(y) was studied. The specimens, with different heat treatment, quenching and thermal refining, were tested in fatigue-testing Machine to study the influence of heat treatment on the metal magnetic memory signal Hp(y). The curve of da/dN ~ Hp(y) was built.

Crystallographic Orientation Dependence of Fatigue Crack Propagation Behavior in Rolled AZ31 Magnesium Alloy

This paper deals with fatigue crack propagation behavior of rolled AZ31B magnesium alloy. Two types of specimens with the loading axis parallel to rolling direction were machined; fatigue crack propagation direction was parallel to transverse direction (L-T specimen), and short transverse direction (L-S specimen). Fatigue crack propagation tests were performed with center cracked plate tension specimen with stress ratio R=0.1 and frequency of 10Hz at room temperature. Crack propagation rate of L-T specimen was approximately 10 times higher than that of L-S specimen. SEM-EBSD observations revealed that the c-axis direction is unfavorable for the fatigue crack propagation in textured polycrystalline magnesium alloy.