Fracture Behavior Of Materials Research Articles

Empirical Rule of Fruit Rind Fragmentation in Muskmelon Netting

The suberized netting tissue on the surface of muskmelons is a remnant of the rind fragmentation caused by the mechanical imbalance between the expanding flesh meat and the solidified epidermis during growth. The appearance of this netting pattern is an important indicator for assessing the quality of muskmelons; however, very few quantitative studies have been conducted on the geometry of the netting. This study statistically analyzed the areas of fine epidermis fragments surrounded by the net using image analysis and explored a common rule governing the probability distribution of the fragment area. We found that the fragment area distribution follows a universal law by the modified Bessel function, which is consistent with the theoretical argument for the fracture behavior of brittle materials.

Spatial Series and Fractal Analysis Associated with Fracture Behaviour of UO2 Ceramic Material

SEM micrographs of the fracture surface for UO2 ceramic materials have been analysed. In this paper, we introduce some algorithms and develop a computer application based on the time-series method. Utilizing the embedding technique of phase space, the attractor is reconstructed. The fractal dimension, lacunarity, and autocorrelation dimension average value have been calculated.

An improved four-parameter conjugated bond-based peridynamic method for fiber-reinforced composites

The classical bond-based peridynamic (BB-PD) theory has inherent limitations on material properties when dealing with composites. An improved lamina conjugated BB-PD model with four independent material parameters is established to study the fracture behavior of composite materials. The model defines four basic generalized PD bonds, including fiber bond, matrix bond, fiber-matrix conjugated bond pair and matrix-matrix conjugated bond pair. Using the equivalent relationship of elastic strain energy density, the analytical expressions of the four micro-modulus in the improved lamina conjugated BB-PD model are determined. These four micro-modulus parameters can describe the four independent engineering material constants of the lamina, which eliminates the restriction of Poisson’s ratio and shear elastic modulus for the composite materials. Moreover, an energy-based failure criterion is further proposed for the failure analysis of composite materials. In order to verify the capability and applicability of the proposed model, the displacement field and fracture behavior of the composite lamina with uniaxial tensile are simulated. In addition, the failure modes and crack propagation path of the laminae with different fiber orientations and initial crack angles are investigated by using the proposed model.

Dynamic fracture analysis in nonhomogeneous piezoelectric materials with a new domain-independent interaction integral

In order to comprehend and forecast the dynamic fracture behaviors of piezoelectric materials, dynamic intensity factors (IFs) are crucial fracture parameters. It is a challenge to effectively calculate the dynamic IFs of the piezoelectric materials containing complicated elastic and/or electric interfaces. For piezoelectric materials with nonhomogeneous properties or even random interfaces, a dynamic domain-independent interaction integral (DII-integral) is established to assess the dynamic stress intensity factors (SIFs) and the dynamic electric displacement intensity factor (EDIF). Furthermore, it is theoretically demonstrated that random interfaces in the integration domain have no effect on the efficiency of the DII-integral and it does not include any derivatives of electromechanical characteristics. The extended finite element method (XFEM) is integrated with the dynamic DII-integral method to study typical cracked piezoelectric specimens exposed to electromechanical impact loads. A wonderful consistency is obtained by evaluating the current results with the relevant literature. Good domain-independence of the proposed dynamic I-integral is verified for nonhomogeneous and discontinuous piezoelectric properties (relative deviation < 1 %). The numerical simulations show the amplitudes of the dynamic SIFs and EDIF are highly affected by the polarization direction. In general, the density has an obvious influence on the peak occurrence time of the dynamic SIF and EDIF. The dielectric permittivity impacts the EDIF evidently, however, the SIF marginally. On the contrary, the piezoelectric coefficient obviously impacts the SIF and EDIF. The elastic stiffness has a considerable impact on the SIF but a minor one on the EDIF.

A technical approach toward pre-crack generation and its effect on the fracture behavior of polymeric materials

Regarding the urgent need for a proper pre-crack generation method in polymeric materials, this study addressed the design and fabrication of a broaching machining apparatus. The performance of this device was examined by preparing polyvinyl chloride (PVC) samples with high sensitivity to the crack-tip radius. Pre-cracks generated by broaching and slotting and then examined by SEM analysis. The fracture parameters were determined by the essential work of fracture (EWF) method. Studies indicated that the energy required for crack growth was on average 24 % lower in the broached samples, suggesting a higher stress concentration in the crack-tip by the broaching approach. The numerical analysis also revealed the more coincidence of the modeled energy values with the broaching method results, further highlighting the higher resemblance of the cracks made by this method to the ideal cracks. Interestingly, the radius of the plastic region in the slotting method was three times larger than in the broaching method, indicating the sharper tip of the pre-cracks in the broaching method. The application of the broaching method for pre-crack generation can lead to more accurate results in the mechanical fracture tests.

A rate-dependent damage model to characterize dynamic fracture behavior of Ti6Al4V under high strain rate loading

Material damage and fracture behavior are affected by loading rates. This paper aims to investigate dynamic deformation and fracture mechanisms of Ti6Al4V over a wide strain rate range from quasi-static to 104 /s. A high strain rate test apparatus is developed and a new rate-dependent material damage law is proposed. The damage energy of Ti6Al4V keeps nearly constant at the strain rate lower than 10 /s, while it declines dramatically under the strain rate high than 103 /s. Ductile to brittle transition of Ti6Al4V occurs at the strain rate of 16,000 /s, which leads to the transition of material fracture mechanism from adiabatic shear to embrittlement fracture. The research proves that developing appropriate damage evolution law is important to improve prediction accuracy of material deformation and guarantee structural design safety especially for dynamic loading components.

Examining the effect of crack initiation angle on fracture behavior of orthotropic materials under mixed-mode I/II loading

In this research, the maximum strain energy release rate concept is adapted for predicting the fracture response of orthotropic materials under mixed-mode I / II loading with an arbitrary precrack-fiber angle. Adaptive maximum strain energy release rate criterion (AMSER) is derived using the crack tip stress field of orthotropic materials with a precise look on the crack initiation direction. In precrack along the fibers, the crack initiation angle is assumed to be in the direction of maximum strain energy release rate (SER). Several experimental observations on a macroscopic scale prove that in the arbitrary angle between the precrack and fiber case, precrack kinks and propagates along the fibers; thus in the derivation of AMSER, crack initiation angle is considered as a superposition of the angle between precrack and fibers and the predicted angle based on the SER criterion (θC). The main purpose of this paper is to investigate the effect of crack initiation angle on the predicted fracture behavior. Due to the arbitrary angle between precrack and fibers, it is impossible to establish pure mode I conditions and derive pure mode I stress intensity factor. Thus, the equivalent fracture toughness concept in pure mode I is presented. AMSER criterion is validated by comparing fracture envelope curves with available experimental data in mixed-mode I / II loading. It can be concluded that accurate prediction of the crack initiation angle based on SER criterion causes the fracture behavior of orthotropic materials to be extracted with high accuracy. The results prove that the hypothesis of precisely predicting crack initiation angle based on the superposition of kink and θC angles complies with the nature of fracture of orthotropic materials.

Variational crack phase-field model for ductile fracture with elastic and plastic damage variables

Based on the study on characteristic features of existing crack phase-field (PF) models for ductile fracture, we propose a new model endowed with elastic and plastic damage variables. In the review part, the emphasis is placed on the plastic driving force and degrading fracture toughness that enable PF models to represent damage evolution in elastoplastic materials. Attention is also paid to the damage evolution tendency in terms of the definition of the yield function. Based on the reviewed features, we originally formulate the proposed model, which separately accommodates two damage variables for elasticity and plasticity. Its constitutive work density consists of elastic, plastic hardening, and damage hardening components. Evolution laws for plasticity and damage are derived by using separate threshold (yield) functions while having similar formats so that those for damage hold variational and thermodynamic consistencies. Also, the proposed model is equipped with thresholds and coefficients to control the amount of damage driving force. Several numerical examples are presented to demonstrate the characteristic features of the proposed model and the ability to mimic the typical fracture behavior of elastoplastic materials.

The experimental methods and elastic properties of shale bedding planes materials state-of-the-art review

The identification of physical properties and fracture behavior of shale or hydrocarbon materials has grown to have substantial importance in the last four decades to industry and investigators alike due to its importance in unconventional oil and gas resources. This interest deviates from shale being a transversely isotropic material formed by bedding layers with different orientations and isotropic properties. In this paper, the experimental setup and the mechanical properties of shale materials have been reviewed. The investigator shows that the properties of shale are not unique, and it is highly dependent on, volume, loading type, and geolocation. Furthermore, the investigator utilized different experimental setup methods to identify the elastic properties of shale and the most common methods are Transducers Strain Detection, Strain gauges, Ultrasonic, and Digital image correlation that is shown in detail.

The effect of the ratio of the radius of the hole and crack length on the multi‐field behaviors of thermoelectric materials under oblique loads

AbstractThis paper establishes a defect model of thermoelectric materials that the oblique multi‐field loads are applied along an arbitrary direction with the crack initiated from a circular hole, and gives both analytical solutions and finite element method (FEM) simulation. On the one hand, in virtue of the conformal mapping function and the Cauchy integral formula, the analytical solutions of electric current density, energy flux, and stress are obtained. Furthermore, the thermoelectric field intensity factors (TEIFs) and the stress intensity factors are also attained. Most notably, we apply the extreme value theorem of multivariate function to explore the effect of the ratio of the radius of the hole, R, and crack length, L, on the fields’ intensity factors of thermoelectric materials under oblique multi‐field loads. Importantly, the maximum value of the mode‐II stress intensity factor (SIF) is obtained when . On the other hand, the finite element simulation is used to explore the fracture behaviors of thermoelectric materials. The analytical solutions and the finite element simulation results are consistent. The effects of the oblique multi‐field loads on the thermoelectric field and the stress field at the crack tip are detailed. The concentration phenomenon of the thermoelectric field and the stress field at the crack tip are influenced by the radius of the circular hole, the crack length, and the directions of the loads.

Determination of Translaminar Notch Fracture Toughness for Laminated Composites Using Brazilian Disk Test

This paper evaluates the fracture of notched epoxy matrix composites using the Brazilian disk (BD) test from both numerical and experimental points of view. The study began with a comprehensive experimental program covering three different composite lay-ups (quasi-isotropic, unidirectional, and cross-ply) and various geometries of U and V notches. Specifically, the BD samples combined the three layouts, four different notch angles, and three notch radii with three specimens per combination, leading to an overall number of 108 fracture tests. The experiments showed the appropriateness of the BD test for the study of the fracture behavior of composite materials and provided a good pool of data for further investigations. Subsequently, the virtual isotropic material concept (VIMC) was applied in combination with two fracture criteria to theoretically predict the experimentally acquired fracture loads. This study demonstrated that using the VIMC approach can provide robust predictions while incurring much lower computational costs compared to the conventional approaches found in the literature.

Fracture behaviour of fibre-reinforced composite materials subjected to shear loading: An experimental and numerical study

Compared to fibre-dominated behaviour, a response dominated by the matrix under shear loading can considerably limit the load-bearing capability and restrict the utilisation of composite materials. It is therefore practically significative to understand the shear response of composite materials. This paper presents a detailed experimental and numerical investigation on the fracture behaviour of composite laminates subjected to shear-dominated loading. Composite specimen with a lay-up of [(0/90)4/0]S are tested using the V-Notched Rail (VRS) shear test method. Subsequently, the Scanning Electron Microscope (SEM) investigation is also conducted on the fracture surfaces of the tested specimens to get insights into the damage mechanisms due to shear loading. In addition, a high-fidelity computational damage model is developed to predict the shear fracture behaviour of fibre-reinforced composites. Simulation results, including loading response, strain distribution and shear fracture, well correlated with experimental results, which demonstrates the predictive capability of the developed elastic-plastic damage model.

Experimental Study on the Damage Characteristics and Fracture Behaviour of Rock-like Materials with Weak Interlayer Zones

To study the effect of the dip angle of the weak interlayer zone (WIZ) on the damage characteristics and fracture behaviours of rock-like samples, a series of uniaxial compression tests were conducted, accompanied by acoustic emission (AE) tests and the digital speckle correlation method (DSCM). The experimental results indicate that the stress—strain curves before the peak can be divided into plastic—elastic—plastic and elastic—plastic curves, and the stress—strain curves after the peak can be divided into plastic failure, transitional failure and brittle failure curves. The relationship between the peak stress and peak strain and WIZ angle can be well described by two linear functions. As the angle increased, the specimen gradually changes from tensile failure to shear failure, and the number of cracks and falling fragments decreases gradually. In addition, it becomes difficult to predict rock mass failure by AE when the WIZ angle is close to 60°. The AE counts decrease with an increasing angle, reach a minimum at 60°, and then increase. Furthermore, the WIZ plays a key role in the deformation of upper hard rock.

Acoustic and thermal energy evolution of AZ31B magnesium alloy under static tensile deformation

Based on the complexity of material damage and fracture behavior, the tensile deformation process of AZ31B magnesium alloy is characterized by infrared thermography (IR) and acoustic emission (AE) these two non-destructive technologies, and using in-situ EBSD technology to explore microstructure evolution under different tensile strains simultaneously. The results show that in the process of tensile deformation, the degree of strain hardening increases continuously with the deformation, and the deformation mechanism of the material changes from basal slip to pyramidal slip and {10–12} tensile twinning. The tensile deformation stage presents different signal characteristics. Using fracture mechanics and the energy release law of materials, combined with temperature and AE signal fluctuations, the transformation of the deformation mechanism, the degree of work hardening, and the dangerous zone during the entire tensile process can be effectively captured.

Towards understanding deformation and fracture in cementitious lattice materials: Insights from multiscale experiments and simulations

Tailoring lattice structures is a commonly used method to develop lattice materials with desired mechanical properties. However, for cementitious lattice materials, besides the macroscopic lattice structure, the multi-phase microstructure of cement paste may have substantial impact on the mechanical responses. Therefore, this work proposes a multi-scale numerical modelling method to simulate the deformation and fracture behavior of cementitious lattice materials, such that the influence of cement paste microstructure can be properly captured. On the microscale, the load–displacement response of cement paste is numerically simulated then experimentally validated. In order to rationally investigate the role of cement paste microstructure, the obtained load–displacement response was then formulated to several types of model inputs reflecting different degree of brittleness. These inputs were then used for simulating the mechanical response of macroscale cementitious lattices. By comparing the simulation to experiment, multi-linear behavior (ML) was found to an appropriate method to include the realistic pre-critical cracking and post-peak softening of cement paste in the model. Compared to ideally brittle behavior, using ML as input, the discrepancy between simulated and experimentally tested fracture energy decreases from 37.4% to 12.4%. In addition, the influence of lattice structure on the strength of cementitious lattices was also accurately captured by the proposed model. Randomized cementitious lattice has 21.6% (22.0% from simulation) lower strength than regular lattice. Moreover, the influence of fracture criterion of the proposed model is discussed and elaborated. Owning to the high simulation accuracy, the proposed multi-scale method in this work could be helpful for tailoring the fracture cementitious lattice materials for future studies.

Applying the new experimental midpoint concept on strain energy density for fracture assessment of composite materials

A mixed-mode I/II fracture criterion for predicting the fracture response of composite materials is proposed. This criterion is derived based on a comprehensive study and the consideration of the physics of fracture onset. The fracture phenomenon that causes the various damage mechanisms at the vicinity of the crack tip is examined. It is elucidated that the stress distribution at the crack tip ought to be defined using the reinforcement isotropic solid (RIS) stress state. This new criterion, which is called Improved Strain Energy Density with Mid-point (ISEDM), includes the effect of the fracture process zone (FPZ) and T-stress, which remarkably affect the mixed-mode fracture process, particularly, when mode II is dominant. Substituting the strain energy density in a pure mode I with the strain energy density in the midpoint of mixed-mode I/II is the creative idea employed in proposing this criterion. Because in pure mode I the effects of FPZ are minimal, change of fitting point on fracture limit curve (FLC) from KIc to midpoint critical stress intensity factors (CSIF’s) makes it possible to consider the effects of FPZ more accurately. In the ISEDM criterion, fracture behavior depends on mechanical properties and CSIF’s of the midpoint. Crack initiation angle is considered along minimum strain energy density and this angle is derived in the midpoint of mixed-mode I/II. RIS theory is used as an applicable theory for modeling orthotropic materials in this paper and causes valid and reliable fracture behavior to be extracted. In addition, changing fracture point from pure mode I to the mid-point of experimental data causes the effects of FPZ to be considered without estimating the toughening mechanisms in this zone, and the fracture behavior is extracted with higher accuracy. FLC’s in comparison with available experimental data prove that the ISEDM criterion anticipates the fracture behavior of orthotropic materials well. Finding KIIc based on the analytical method is a valuable achievement. In this article, KIIc can be predicted with appropriate accuracy, only by CSIF’s of mid-point and using ISEDM criterion.

In Situ Measurement of the Strain Field at the Fatigue Crack Tip Based on Sub-Image Stitching and Matching DIC.

Studying the in situ measurement and evolution of the strain field at the crack tip during fatigue crack growth (FCG) is of great significance for understanding the fracture characteristics of materials and predicting fatigue life. Herein, a new method is proposed for the in-situ measurement of the strain field at the fatigue crack tip based on microscopic digital image correlation (DIC). The method proposed solves the problem of the existing in situ strain field measurement method being unable to dynamically track the crack tip and take the crack tip image due to the limitation of the field of view of the microscopic camera. A macroscopic camera is used to capture the global crack images on one side of the compact tension (CT) specimen. Meanwhile, a microscopic camera is used to track and capture the crack propagation speckle image on the other side of the CT specimen. The proposed method was verified by experiments with Quenching and Partitioning 980 (Q&P980) steel, and the results showed that the method has high accuracy, with the average measurement error being less than 5% and the maximum error being less than 10%. A butterfly shape of the measured strain field and the strain concentration near the crack tip were observed. The success of this method will help to obtain better insight into and understanding of the fracture behavior of metal materials as well as precise prediction of the fatigue life of metal materials.

Damage criterion approach to high‐strength steel RHS truss joints

AbstractThis paper describes finite element simulations of the structural deformation and material fracture behaviour of high‐strength steel RHS K gap truss joints. The fundamental scope was to examine whether the joint strength predictions based on the behaviour of lower strength and more ductile steel with a yield stress of 355 MPa or less would hold good for higher strength 450 MPa steel with a lower ductility. The FEA reliability analysis indicates that for failure modes associated with local buckling, yielding and deformation (chord side wall failure, chord face plastification and brace failures due to reduced effective width), the existing approach could, with modifications, be extended to cover higher strength tubes, but for failure modes associated with fracture or ductility or modes liable to brittle failure (tearing in the tension brace and chord punching shear), a strength reduction modifying factor was required. The finite element simulations incorporated a damage mechanics approach to calibrate experimental results in both the fracture and deformation modes of failure. The paper proposes a new formulation for strength and incorporates reduced ductility in high‐grade steel with a modifier function that is not based on yield stress, instead recognizes the reduced ultimate strains, damage parameter for fracture and ultimate stress of the material.

Assessment of dynamic mode-I delamination driving force in double cantilever beam tests for fiber-reinforced polymer composite and adhesive materials

The double cantilever beam (DCB) tests are widely used to assess the interfacial delamination properties of laminated composites. For quasi-static loads, the DCB tests are standardized based on the beam mechanics; for dynamic loads, however, such as high-loading-rate impact and cyclic loads, there is no established analytical theory. This presents a significant obstacle preventing the research community from assessing the delamination behavior of composites or adhesives for their application under complex in-service loads. In this paper, the theory of evaluating dynamic mode-I delamination driving force for DCBs under general displacement loads is developed for the first time, accounting for structural vibration effects. The developed theory is demonstrated by two examples: high-loading-rate split Hopkinson bar impact and cyclic fatigue loads. The analytical solutions are validated by published experiment results and in-house tests. This work provides a fundamental analytical tool to study and assess the fracture behavior of fiber reinforced-polymer composite and adhesive materials under various loading conditions.

Parameter identification method of the semi-coupled fracture model for 6061 aluminium alloy sheet based on machine learning assistance

The ability to describe the fracture behaviour of materials and the difficulty of parameter calibration are important factors for evaluating the ductile fracture criterion. To find a ductile fracture criterion that can balance both these factors, in this study, the fracture behaviour of 6061 aluminium alloy was characterized based on a semi-coupled damage mechanics framework, and a parameter identification method based on machine learning assistance was proposed. Using this method, the calibration method of the damage initiation model was improved to fully consider the non-linearity of the loading path. Moreover, the calibration process of the fracture and damage evolution models was replaced by the neural network model. The results indicated that the semi-coupled fracture model can accurately predict the damage initiation, accumulation, and fracture of the 6061 aluminium alloy during the forming process. The parameter identification method based on machine learning assistance can circumvent the process of extracting the stress state evolution from the numerical models of calibrated specimens; a set of reliable parameters can be extracted from the force–displacement response using only one specimen. The combination of the semi-coupled fracture model and parameter identification method provides a new approach to balance the difficulty of parameter calibration and the description ability of the ductile fracture criterion.