Fracture Toughness Of Materials Research Articles

Mechanical and failure analysis of thick composites under hygrothermal conditions by a novel coupled hygro-thermo-mechanical multiscale algorithm

A novel coupled hygro-thermo-mechanical multiscale-APFEA (HTM-multiscale-APFEA) algorithm is developed to precisely predict the mechanical and failure behavior of thick fiber-reinforced laminated composites under hygrothermal conditions. The Fourier and Fick's equations are simultaneously solved by the proposed fully-coupled temperature-moisture concentration (FCTM) algorithm to account for their mutual effects on each other. Two subroutines, one responsible for the homogenization, failure analysis, and also linking the macro and micro models of the composite material, and another for establishing the constitutive equations and failure analysis of the cohesive/adhesive material, are integrated into a user-defined material code extended for also defining the materials failure behavior. The effects of temperature and moisture conditions on the stiffness, strength, coefficients of hygrothermal expansions (CHEs), and fracture toughness of matrix and cohesive/adhesive materials are considered. The results of the HTM-multiscale-APFEA algorithm are verified against the results of experimental data, analytical high-order theories, and reliable numerical analysis. Furthermore, the failure analysis of composite laminate under hygrothermal conditions coupled with mechanical loading (bending) is carried out by the HTM-multiscale-APFEA algorithm, and compared with experimental data. The results have shown that the transverse tensile strength, shear strength, and transverse Young's modulus of the composite material degrade respectively about 72%, 13%, and 40% in the most severe hygrothermal conditions at the material boundaries; while the normal stiffness and normal strength of the cohesive/adhesive material decline by about 73% and 47%, respectively, at outer layers. In addition, the mixed-mode fracture toughness of the adhesive material elevates from 0.55 ×103N/m at inner layers to 2.14 ×103N/m at outer layers of adhesive material. The proposed algorithm is highly flexible and can easily be adapted to model different types of laminated composites.

A theoretical model of fracture of biological composites considering complex structural arrangement of microstructures

Although it is known that biological materials have remarkable fracture strength and toughness, the underlying mechanisms have not been fully understood. A key question is what effects of the structural arrangement of the microstructure are in biological materials. To address this problem, we developed a fracture model based on the fundamental solutions of the crack and rigid line inclusions in matrix to consider the roles of the complex arrangement of the microstructure. Firstly, we obtained the analytical solutions of the SIFs of three basic problems with two inclusions. These solutions revealed several fundamental toughening mechanisms of biological composites via controlling the geometric arrangement of microstructures. Then, we analyzed the fracture problem of multiple rigid lines and cracks with one-level of hierarchy of composite structure. We found that the large aspect ratio of rigid lines produces significant stress shielding effect on the main crack, but it simultaneously creates high possibility of producing local microcracks therein. Interestingly, these microcracks can significantly reduce the SIFs of the rigid lines, while only slightly increases the SIF of the main crack. Finally, we studied the effect of the hierarchical structure on the fracture toughness of biological materials. Compared with the one-level structure, the two-level hierarchy can effectively reduce the SIF of the main crack, and at the same time it becomes less sensitive to the change of the geometric parameters of the microstructures at higher level. This study may provide guidelines for the structural design of advanced biomimetic materials.

A temporal averaging–based approach to toughness homogenisation in heterogeneous material

A new approach to defining the effective fracture toughness for heterogeneous materials is proposed. This temporal averaging approach is process dependent, incorporating the crack velocity and material toughness. The effectiveness of the new technique is investigated in the context of hydraulic fracture through heterogeneous rock with a periodic material toughness. The plane strain model is considered without fluid leak-off, to more easily investigate different regimes (toughness/viscosity). Numerical simulations are used to examine the effectiveness of the new homogenisation strategy, with comparison against the recently proposed maximum toughness strategy. Simulations are conducted using an extremely effective (in house-built) time–space adaptive solver. The regimes in which each strategy is effective are determined.

The Effect of the Petrography, Mineralogy, and Physical Properties of Limestone on Mode I Fracture Toughness under Dry and Saturated Conditions

Determining the fracture toughness of rock materials is a challenging, costly, and time-consuming task, as fabricating a sharp crack in rock specimens will lead to failure of the specimen, and preparing specimens for determining the rock fracture toughness requires special equipment. In this paper, the relationship between mode I fracture toughness (KIC) with the rock index properties, mineralogy, and petrography of limestone is investigated using simple nonlinear and simple/multiple linear regression analyses to provide alternative methods for estimating the fracture toughness of limestones. The cracked chevron notched Brazilian disk (CCNBD) method was applied to 30 limestones with different petrographic and mineralogical characteristics under both dry and saturated conditions. Moreover, the index properties of the same rocks, including the density, porosity, electrical resistivity, P and S wave velocities, Schmidt rebound hardness, and point load index, were determined. According to the statistical analyses, a classification based on the petrography of the studied rocks was required for predicting the fracture toughness from index properties. By classifying the limestones based on petrography, reliable relationships with high correlations can be introduced for estimating the fracture toughness of different limestones using simple tests.

Densification of WC-Fe-Ni-Co-Cr cemented carbides processed by HIP after sintering: effect of WC powder particle size

Shrinkage, liquid formation and mass losses of WC-19 vol% FeNiCoCr alloys during sintering have been investigated in compositions either with coarse or submicron WC powders. Mass losses detected by thermogravimetry are compatible with carbothermal reduction of the different oxides present in the powder mixtures. Hardness and fracture toughness of materials based on submicron WC powders are within tolerances of those reported for WC-Co materials with similar microstructures. However, fracture strength is approx. 25% lower.

Deformation Performance and Fracture Toughness of Carbon Nanofiber Modified Cement-Based Materials

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Time-temperature superposition principle for the shear fracture behaviour of soft adhesive layers: From bulk to interface

Soft adhesive layers have attracted great attention as a commonly used adhesive technique, particularly because of their shear fracture behaviour at extreme loading rates and temperatures. Therefore, the present study examined the shear fracture properties of a soft adhesive layer through systematic rheological experiments, loading-unloading shear tests and shear fracture tests. Due to a similar viscoelastic characteristic in rheological properties and fracture properties, the time-temperature superposition principle (TTSP) was extended from the bulk to the interface to investigate its shear cohesive failure. A shear fracture toughness master curve was defined using the time-temperature equivalence shift factors derived from the rheological properties. The shear fracture behaviour of the soft adhesive layer could be predicted using data from a narrow range of loading rates/temperatures. The results demonstrated the potential of extending the TTSP approach from the bulk to a soft adhesive layer having viscoelastic character, which might be utilised to predict the shear fracture toughness of soft adhesive materials under extreme conditions.

The Dislocation Mechanics of Crystal/Polycrystal Plasticity

A brief history and update are given in four examples demonstrating that polycrystals are generally stronger than their individual component crystal grains because of obstructed dislocation pile-ups at grain boundaries. The example cases constitute diverse applications of a Hall–Petch dependence involving one or another aspects of the full polycrystal stress–strain behavior: (1) a Hall–Petch based description for a compilation of delayed yielding measurements compiled for steel; (2) computations for an H-P grain size dependent, tensile, plastic instability behavior of copper; (3) an H-P relationship for the true maximum stress for the limit of uniform straining of aluminum; and (4) the onset of a ductile-to-brittle transition in steel cleavage fracturing measurements that are connected to the material fracture toughness properties.

Effects of graphene content on the microstructure and mechanical properties of alumina-based composites

In this work, alumina-graphene (Al2O3-G) composites with graphene contents ranging from 0.5 to 3% were prepared by stepwise feeding ball milling and hot pressing. The influences of graphene content on the microstructure and mechanical properties of Al2O3-G composites were investigated. Results showed that the densification, grain sizes, flexural strength, fracture toughness and Vickers hardness of materials increased firstly and then decreased with increasing graphene contents. When the graphene content was 1%, the value of each performance parameter reached the maximum. The average grain size of material decreased from 991 to 551 nm as the graphene content increased from 0 to 1%, but it increased to 863 nm when the graphene content was 3%. The flexural strength, fracture toughness and Vickers hardness of composites with graphene content of 1% increased to 763.5 MPa, 7.4 MPa m1/2 and 21.28 GPa. Compared with the Al2O3, the fracture strength and toughness of the composites increased by up to 54.63 and 65.54%. Analysis suggested that the strength of Al2O3-G composites was mainly related to the grain size and preexisting microflaws.

Texture and Grain Boundary Network Evolution of Laser Powder Bed Fusion Processed Pure Ni During Post-printing Annealing

Commercially pure Ni was additively manufactured using laser powder bed fusion. The printed specimens were then subjected to annealing treatments in a range of 700 °C to 1200 °C to investigate the evolution of the microstructure using electron backscatter diffraction mapping and a five-parameter analysis of the grain boundary character distribution. The post-printing annealing treatment resulted in microstructural changes in respect to grain shape and size, the grain boundary character distribution and the overall texture. However, the extent of these changes strongly depended on the annealing temperature. The grain structure and overall texture changed only modestly when annealed below 900 °C. The grains grew by about 10 pct and this led to a small (≈ 15 pct) increase in the areas of boundaries with low energy (111) planes at the expense of higher energy grain boundary planes with the (001) orientation. Static recrystallization was the dominant microstructure evolution mechanism at annealing temperatures greater than 1000 °C, where new equiaxed grains replaced the initial printed microstructure, enhancing the relative areas of low energy grain boundaries (i.e., sum 3 and sum 9) by a factor of more than five. This change increased the population of boundaries with the low energy (111) plane by a factor of five and decreased the strength of the texture by more than 50 pct through twinning. The resultant microstructure is expected to ultimately improve the material properties, where the increase in the relative areas of sum 3 boundaries would enhance the corrosion resistance and fracture toughness of material, and the texture weakening diminishes the anisotropy in mechanical behaviour.

Experimental-numerical analysis of the fracture process of Al-Al-Ti laminated composite

In the paper presented a study of the fracture process of explosive welded layered material AA2519-AA1050-Ti6Al4V (Al-Al-Ti laminate) at ambient (+20 °C) and reduced (−50 °C) temperatures. The tensile tests and fracture toughness tests were conducted for both types specimens made of base materials plates and of laminated plate. During tensile tests performed on flat specimens the signals of loading force (P) and specimen extension (uext) were recorded. The signals of loading force (P), specimen deflection (udef) and the crack mouth opening displacement (COD) were recorded while performing the tests on fracture toughness of materials on SENB type specimens. The breakthroughs of the tested specimens were observed by scanning electron microscope (SEM).The results obtained during the experimental tests indicate the complicated nature of the cracking process of specimens from the Al-Al-Ti laminate. The deviation from linearity was observed during loading on the sections where it should be linear. There were also slightly decreases in the force value during the load. During macro observation of the fractured surfaces of SENB specimens, delamination cracks between the Al and Ti layers are clearly visible. The size of these cracks increases as the test temperature decreases. The SEM observations clearly indicate that the delamination crack is formed in the AA1050 layer joining the Ti6Al4V and AA2519 base materials. Precise observation by SEM allowed to establish that the development of a delamination crack begins with different type of particles fracture and material discontinuous in narrow strip (20–40 mm) near at Ti6Al4V material. Then the delamination crack develops in the layer of AA1050 material according to a shear mechanism.In order determine the stress and strain distributions in tested specimens the they numerical models were developed and simulation of loading were performed by ABAQUS program. The results of stress and strain distributions obtained clearly shows on large differences they values in the different layers of the laminate. Maximal differences of stress levels occurs between layers Ti6Al4V and AA1050 materials. Due to the fact that the material of the connecting layer (AA1050) has a low level of yield strength, a very high level of plastic strain occurs.Based on the results obtained during the experimental tests, SEM observation of fracture surfaces and numerical calculations, it can be concluded that the weakest area in the tested laminate is the connecting layer AA1050. Namely is it, a thin strip between AA1050 and Ti6Al4V, which consists of metal base particles, intermetallic compounds, their oxides and discontinuities of the material in form of voids.When using this type of laminate, special attention should be paid to the strength of the AA1050 bonding layer.

A novel logarithmic approach to generate new probability distributions for data modeling in the engineering sector

In this paper, we introduce a new statistical methodology for updating the flexibility level of the traditional distributions. The newly developed method is called, the logarithmic-U family of distributions. For the logarithmic-U distributions, the estimation of the parameters via the maximum likelihood method is discussed. Some mathematical properties of the logarithmic-U distributions are also derived. By using the logarithmic-U method, an updated version of the Weibull model, namely, the logarithmic Weibull distribution is introduced. A simulation study for the logarithmic Weibull distribution is provided. Finally, the practical illustration of the logarithmic Weibull distribution is shown by analyzing two data sets taken from the engineering sector. The first data set represents the fracture toughness of Al2O3 material. Whereas, the second data set represents the fatigue fracture of Kelvar 373/epoxy. The practical applications show that the proposed logarithmic Weibull distribution is very competent for analyzing data sets in engineering and other related sectors.

A new spherical indentation approach to determine fracture toughness of high strength steels

Fracture toughness indicates the resistance to unstable crack growth that is very important in the assessment of structural integrity. As the Instrumented Indentation Test (IIT) technique is relatively simple to perform, it has been suggested as an alternative way to determine fracture toughness of engineering materials. This paper presents a new spherical IIT approach to predicting fracture toughness of engineering materials using the critical contact pressure. Firstly, according to Johnson’s maximum strain energy theory under indentation, the formula of critical contact pressure under IIT is derived by considering strain hardening and fundamental tensile properties. Secondly, by using an automatic iterative procedure of translating the input and output data between MATLAB and ANSYS, finite element analysis is carried out to build a dummy database of critical contact pressure versus strain hardening and tensile properties for a broad scale of engineering materials. Finally, for the sake of engineering applications, a general analytical formula is put forward according to the dummy database, by which the critical contact pressure and thus the critical indentation depth can be read directly. Fracture toughness of engineering materials is then determined using the concept of indentation energy to fracture at the critical indentation depth. Validation of predicted fracture toughness and tensile properties of four high strength steels is taken out using compact tension (CT) and standard tensile tests, respectively. Good agreements are found between the standard tests and IIT.

A comparative study on constraint parameters for characterizing fracture toughness of X60 and X100 pipe steels

The fracture toughness resistance curve (e.g., J-R curve and crack tip opening displacement (CTOD) or δ-R curve) is important in facilitating strain-based design and integrity assessment of oil and gas pipelines, where influence of ground movement and presence of planar weld flaws must be accounted for. In the present study, duplicate single edge notched bend (SE(B)) and clamped single edge notched tension (SE(T)) specimens with two different initial crack lengths were tested at room temperature for longitudinally-oriented specimens machined from X60 and X100 pipe steels where the notch is along the through-thickness direction. The results showed the expected trends of higher fracture toughness resistance curves for shallow-cracked over deep-cracked specimen types and tension over bending loading modes. Eleven constraint parameters (i.e., QHRR, QSSY, QLM, QBM, A2, A2BM, h, Tz, Cp, Ap, Vp) were calculated based on 3-D finite element analysis for all tested SE(B) and SE(T) specimens. The results indicated that the shallow-cracked SE(B) specimens exhibit a constraint condition similar to the intrinsically low-constraint deep-cracked SE(T) specimens made of the X60 pipe steel. Among all of the constraint parameters, the Ap parameter based on the equivalent plastic strain isoline was found to correlate the best to the material fracture toughness for currently tested specimens. Furthermore, a linear master curve between various critical fracture toughness values and Ap parameter was obtained for all the tested specimens with different crack lengths, loading modes and pipe steels.

Stress intensity factors for the double-edge cracked Brazilian disc under compression: Theory and experiment

The true mode II fracture can be achieved by the double-edge cracked Brazilian disc (DCBD) under compression load. The methods to calculate stress intensity factors (SIFs) for the DCBD specimen, however, are only numerical methods at present. The analytical solutions of the mode I and II SIFs in the DCBD specimen under compression are obtained using the weight function method. The compression load is considered as the non-uniformly distributed pressure, including parabolic, quartic polynomial, elliptical, cosinoidal, and semi-periodical cosinoidal pressures. Compared with the numerical methods, the SIFs for the DCBD specimen can be calculated with high accuracy and efficiency by the analytical solutions. The calculation results show that the distribution form of pressure has a great influence on SIFs for the large contact angle and short crack. The normalized mode I and II SIFs in the DCBD specimen under compression are constantly negative for any loading angle, contact angle, and crack length. The effect of contact angle on mode I and II SIFs can be ignored when the relative crack length α ≥ 0.6. The true mode II fracture tends to occur in the DCBD specimen for the small loading angle and long crack conditions. The experiments are carried out by using sandstone DCBD specimens. The true mode II fracture toughness of the sandstone material used in this paper is 0.9383–0.9387 MPa m1/2.

An experimental assessment of fracture toughness in novel crimp‐free‐based composite materials for aerospace applications

AbstractIn the design of structural composite components for aerospace applications, durability and reliability play a very significant role. To assess the reliability of these material it is essential to carry out robust experimental tests on several specimens and under different loading conditions to allow the determination of fundamental fracture parameters. Fracture toughness, in particular, allows the quantification of the material strength to fracture. This work proposes a study on non‐crimp fabric (NCF) together with a two‐component epoxy resin. The selected system has been selected based on its suitability to produce aerospace‐approved components using resin transfer molding (RTM) process. The fabric adopted is a SAERTEX NCF with very high modulus and strength, whereas the resin is BDP 4294. This work shows the methods, equipment, and results of an experimental campaign carried out to determine the fracture toughness of the manufactured NCF composite material. Finally, to quantify the fracture toughness of the NCF composite material, Mode I, II, Mixed Mode I–II, and translaminar fracture tests were also considered.

Evaluation of the interlaminar fracture toughness on composite materials using DCB test on symmetric and unsymmetric configurations

A procedure to measure the interlaminar fracture toughness of a composite material is proposed in this work. This property is evaluated using the DCB test, the new formulation developed being applicable to small thicknesses and nonsymmetric configurations. The GC evaluation proposed in this paper does not require to know the evolution of the crack length with the load. This fact facilitates the performance of the test and allows complex situations (crack jumps, tests at high temperature,…) to be taken under consideration. An experimental campaign has been carried out on four different configurations, three symmetric (2 + 2, 4 + 4 and 8 + 8 layers) and one nonsymmetric (4 + 8 layers). The results show that, when they are appropriately treated, the values obtained are independent of the number of layers of the adherents and even of the symmetry of the joint, validating the use of the DCB test on nonstandardized coupons.

A Comparative Study to Evaluate the Essential Work of Fracture to Measure the Fracture Toughness of Quasi-Brittle Material.

In the present work, three different woven composite laminates were fabricated using the hand lay-up method. The woven reinforcement fibres were carbon fibres (CFRP), glass fibres (GFRP-W) and (GFRP-R) in combination with epoxy resin. Then, the central notch specimen tensile test (CNT) was used to measure the fracture toughness and the corresponding surface release energy (). Then, the data were compared with the essential work of fracture (we) values based on the stored energy of the body to obtain a new standard fracture toughness test for composite laminates using relatively simple techniques. In addition to an extended finite element model, XFEM was implemented over a central notch specimen geometry to obtain a satisfactory validation of the essential work of fracture concepts. Therefore, the average values of () were measured with CNT specimens 25.15 kJ/m2, 32.5 kJ/m2 and 20.22 kJ/m2 for CFRP, GFRP-W and GFRP-R, respectively. The data are very close as the percentage error for the surface release energy measured by the two methods was 0.83, 4.6 and 5.16 for carbon, glass and random fibre composite laminates, respectively. The data for the fracture toughness of XFEM are also very close. The percentage error is 4.6, 5.25 and 2.95 for carbon, glass and random fibre composite laminates, respectively. Therefore, the fundamental work of the fracture concept is highly recommended as a fracture toughness test for composite laminates or quasi-brittle Material.

Fracture analysis of chiral fiber-reinforced biocomposite

The widely presented chiral microstructures in biological materials such as wood, bone and climbing tendrils, bring up biological materials with favorable elasticity, fracture toughness and impact resistance. A tricky thing is, how the chiral microstructures could affect the fracture behaviors of this category of materials is not clear. In this paper, a fracture mechanics model of chiral fiber composite under mode I loading is established for investigating the effects of chiral microstructures on the fracture behaviors of corresponding materials. The analytical solutions of the stress and displacement fields near the crack tip are obtained by using the potential function method. The finite element method (FEM) for chiral materials is implemented into ABAQUS and corresponding simulation is conducted. The theoretical results are consistent with those from simulations. The effects of chiral coefficients on the stress concentration and the stress intensity factor are investigated. The results show that the couple stresses induced by the chiral microstructure can significantly decrease the stress concentration near the crack tip. Furthermore, the chiral microstructures can hinder the crack propagation and thus strengthen, to a certain extent, the fracture toughness of the biological materials. It is expected this work can enhance our understanding on the relationship between microstructure and properties of biological materials, and contribute to the biomimetic design and preparation of high-performance materials.

A new fracture toughness calculation method for cementitious materials in the three-point bending test based on the transverse force

The traditional calculation method for the fracture toughness of cementitious materials by the three-point bending test is based on the empirical formula of concrete specimens. There may be some errors in the fracture toughness calculation of cement paste and mortar when the traditional method is applied. In this research, a new fracture toughness calculation method based on transverse force and effective crack model was proposed to calculate the effective crack length of cement paste and mortar, and the fracture toughness was calculated based on experimental data rather than empirical formula. In the new calculation method, the peak point of the transverse force curve can well determine the crack initiation point of the specimen. Based on the three test parameters of crack opening displacement, vertical load, and vertical displacement, the effective crack length and unstable fracture toughness of different specimens can be calculated. The results show that the lower the water-cement ratio and the higher the sand volume fraction, the higher the unstable fracture toughness of the cement paste and mortar. The destabilization point and the crack initiation point of the cement paste are very close, while the two points of the mortar are more distinguishable from each other. The unstable fracture toughness obtained by the new calculation method are slightly lower than those obtained by the empirical calculation method. However, the deviation between the two calculation methods becomes smaller with the increase of the aggregate volume fraction. It can be predicted that if the aggregate volume fraction is high enough, the results calculated by the two methods tends to be consistent.