mode-I Loading Research Articles

Effect of high temperature on mode-I fracture toughness of granite subjected to liquid nitrogen cooling

Liquid nitrogen (LN2) ultra-low temperature fracturing technology has broad application prospects in the storage and transformation of geothermal wells. Therefore, it is of great significance to investigate the fracture toughness of granite samples after elevated temperature treatment and LN2 cooling. In this paper, the Cracked Straight Through Brazilian Disc (CSTBD) granite specimen was heat-treated at different temperatures to study the mode-I fracture toughness of granite after rapid cooling by LN2. Meanwhile, acoustic emission (AE) and digital image correlation (DIC) techniques were used to monitor the deformation and failure process of granite. Our results show that when the heating temperature is more than 400 °C, after LN2 cooling, the internal thermal damage of granite is intensified, the plastic characteristics are gradually enhanced, and the fracture toughness decreases significantly. The DIC results show that, with increasing stress, cracks start to form at the two ends of the pre-crack and propagate to the contact point between the press and rock sample along the loading direction under mode-I loading. Near the peak load, the Von-Mises equivalent strain (Evm) gradually increases, and a high strain band appears along the loading direction. When the heating temperature exceeds 400 °C, the density and width of thermally induced cracks in granite gradually increase after LN2 cooling, the fracture track gradually deviates from the straight line, secondary cracks extend, and the plastic characteristics are enhanced. High temperatures cause thermal damage to the rock, and rapid cooling exacerbates this damage. It can be considered that 400 °C is the critical temperature threshold at which the physical–mechanical behavior and fracture characteristics of CSTBD granite change significantly under the condition of rapid LN2 cooling.

Damage detection in intra-ply glass/carbon laminated composites under Mode-I and Mode-II fracture loadings

A comprehensive experimental investigation was performed to understand damage detection capabilities of intra-ply glass/carbon composites embedded with carbon nanotubes under mode-I and mode-II fracture. Novel modified four circumferential probes were employed on fracture test specimens to capture piezo-electrical response. The effect of three different laminate orientations (G-0-C-90, C-0-G-90, and G-45-C-45) on both mode-I and mode-II fracture initiation toughness and the electrical-fracture response were discussed. C-0-G-90 demonstrated higher mode-I fracture toughness, while G-0-C-90 composites exhibited higher mode-II fracture toughness. The fracture toughness values were related with scanning electron microscopy images and electrical response was correlated well with the crack dynamics.

Effect of similar and dissimilar interface layers on delamination in hybrid plain woven glass/carbon epoxy laminated composite double cantilever beam under Mode-I loading

Effect of similar and dissimilar interface layers on delamination in hybrid plain woven glass/carbon epoxy laminated composite double cantilever beam under Mode-I loading has been investigated experimentally and analytically. Glass-glass, glass-carbon interface layers in three different configurations of hybrid plain woven glass/carbon epoxy laminated composites were fabricated. Valvo’s mode partition method from the literature is utilised to compute individual modal contributions and total fracture toughness of the hybrid composite laminates. Mode-I fracture toughness contribution is compared with standard data reduction schemes of ASTM D5528-13. The comparison reveals that Valvo’s mode partition method considers mode-mixity and provides conservative results. The Valvo’s mode partition does not require any correction factors including curve fitting, it provides a straightforward method for evaluating fracture toughness as they are based on the mechanics of composite materials. The comparison of R-curves of hybrid configurations reveal that the insertion of carbon with glass at the interface of symmetric hybrid configuration enhances initial fracture toughness and stabilises whereas, with the change in layer configuration of anyone arm of the double-cantilever beam, the crack growth trend is also affected irrespective of same interface layers. The fractography analysis of delamination surfaces reveals that crack propagation through a resin-rich layer creates a rougher fracture surface resulting in higher energy dissipation as compared to crack propagation through resin-rich pockets.

On the robustness of the stabilized finite element method for delamination analysis of composites using cohesive elements

We demonstrate the ability of a stabilized finite element method, inspired by the weighted Nitsche approach, to alleviate spurious traction oscillations at interlaminar interfaces during composite delamination. The method allows for the use of any value for the cohesive stiffness and obviates the need for ad hoc approaches to estimate the minimum penalty stiffness for accurate analysis. Simulation studies involving constant strain patch tests and benchmark delamination tests under mode-I, mode-II, and mixed-mode loadings show evidence of traction oscillations with the standard method. In contrast, the stabilized method is able to alleviate traction oscillations, which illustrates its efficacy and robustness.

Influence of extremely cold environmental conditions on interfacial fracture phenomenon of aerospace grade unidirectional composites

An investigation of interfacial fracture modelling of carbon fibre reinforced plastic (CFRP) laminates at the atmosphere similar to the cruise condition of an aircraft has been carried out in this article. The Mode I & Mode II fracture tests are carried out using specimen of aerospace grade composite (AS4/914) at−550C. Compliance based methods for estimation of crack growth have been adopted for monitoring during the fracture tests. A new set of thermally influenced interfacial fracture properties are evaluated for AS4/914 laminates. A modified traction – separation law has been derived for Mode-I loadings considering the influence of fibre bridging under influence of extremely cold environmental conditions. This law has been evaluated from the superposition of traditional bilinear law and derived bridging law. A significant reduction in interlaminar fracture toughness has been observed due to the fragile nature of the matrix under cold environment. Experimentally obtained interfacial fracture properties are implemented into the numerical formulation. Extended Isogeometric Analysis augmented with Cohesive Zone Modelling (XIGA-CZM) for unidirectional CFRP laminate has been enhanced and enriched with thermally influenced fracture toughness properties for further investigation. Results obtained from the present XIGA-CZM formulation shows a good agreement with experimentally obtained results. Scanning Electron Microscope (SEM) observation of fractured surfaces are carried out to investigate the nature of crack propagation in CFRP laminate at−550C.

Effect of environmental conditions on fracture behavior of solder joints

Double cantilever beam (DCB) specimens were prepared according to standard surface mount technology (SMT). The samples were stored inside an environmental chamber at two different relative humidity values (i.e. 40 or 100%) for either 2 or 4 h. Then they were aged at 25 °C, 75 °C or 125℃ for the same time. Finally, after being cooled to room temperature, fracture tests were performed under mode-I loading conditions at a strain rate of 0.03 s−1 at room temperature. Storage time did not have a significant effect on the fracture behavior. The fracture load and energy of the solder joints decreased significantly when the temperature was increased from 25 to 75℃. By further increase in the temperature from 75 to 125℃, the fracture strength slightly increased. This behavior was attributed to the thickness of intermetallic compound (IMC) as well as the portion of brittle phases on the joint microstructure. The influence of relative humidity on the fracture strength was less than the temperature effect due to coarsening behavior of microstructure with a humidity rise. The fracture surface of the specimen stored at a temperature of 25℃ and relative humidity of 40% was flat and smooth, while in other cases, the fracture surfaces showed a three-dimensional roughness.

The J-integral for mixed-mode loaded cracks with cohesive zones

The J-integral quantifies the loading of a crack tip, just as the crack tip opening displacement (CTOD) emanating from the cohesive zone model. Both quantities, being based on fundamentally different interpretations of cracks in fracture mechanics of brittle or ductile materials, have been proven to be equivalent in the late 60s of the previous century, however, just for the simple mode-I loading case. The relation of J and CTOD turned out to be uniquely determined by the constitutive law of the cohesive zone in front of the physical crack tip. In this paper, a J-integral vector is derived for a mixed-mode loaded crack based on the cohesive zone approach, accounting for the most general case of a mode-coupled cohesive law. While the J_1-coordinate, as energy release rate of a straight crack extension, is uniquely related to the cohesive potential at the physical crack tip and thus to the CTOD, the J_2-coordinate depends on the solution of the specific boundary value problem in terms of stresses and displacement gradients at the cohesive zone faces. The generalized relation is verified for the Griffith crack, employing solutions of the Dugdale crack based on improved holomorphic functions.

Tufting thread and density controls the mode-I fracture toughness in carbon/epoxy composite

Herein, interlaminar crack initiation and its growth in tufted carbon/epoxy composite under Mode-I loading are investigated for different thread materials and tuft densities. Two configurations of Double Cantilever Beam (DCB) test specimens are fabricated – one with 2 rows of tuft (hereafter referred to as lower tuft density) and another with 3 rows of tuft (will be referred to as higher tuft density). The crack front is arrested and delamination growth is delayed by tufting, which increases interlaminar fracture toughness(GIC). Higher enhancement in fracture toughness is observed for carbon thread tufted specimens followed by Kevlar and then glass thread tufted specimens. Fracture toughness of tufted specimens is about 4.5 to 10 times of untufted specimen depending on the thread material and tuft density. An increase in tuft density increases fracture toughness from 175% for Kevlar to 272% for glass threads. Fiber bridging from the parent laminate layer is observed in the untufted specimen, whereas in the tufted specimen, this phenomenon is insignificant except for bridging due to tufting thread. Fracture analysis shows that the failure is mainly due to the rupture of thread at the interface. Thread pull-out or slippage is absent exhibiting good adhesion with epoxy matrix.

Fracture toughness characteristics of additively manufactured Ti–6Al–4V lattices

Metallic lattice structures are well known for having high specific elastic moduli and strength. However, very little is understood about their resistance to fracture. In this work Ti–6Al–4V lattice structures are additively manufactured by selective laser melting and their fracture toughness characteristics are investigated. Resistance to fracture was determined under Mode-I loading at static rates using an extended compact tension (EC(T)) specimen, modified to contain lattice cells. The lattices consist of octet cells with a 3.5 mm edge length and relative densities ranging from 25% to 56%. Toughness is shown to increase by a power law with relative density and this trend was also obtained with finite element models. A new functional grading optimisation methodology is also presented for increasing fracture toughness. The size optimisation results in a functionally graded lattice whereby lattice truss diameters become the design variables. After size optimisation, initiation fracture toughness increases by up to 37%.

Brittle-fracture simulations of curved cleavage cracks in α-iron: A molecular dynamics study

Although body-centered-cubic (bcc) metals and alloys are ubiquitous as structural materials, they are brittle, particularly at low temperatures; however, the mechanism of their brittle fracture is not fully understood. In this study, we conduct a series of three-dimensional molecular dynamics simulations of the cleavage fracture of α-iron. In particular, we focus on mode-I loading starting from curved crack fronts or the so-called penny-shaped cracks. In the simulations, brittle fractures are observed at cleavages on the {100} plane, while the initial cracks become blunted on other planes as a result of dislocation emissions. Our modeling results agreed with a common experimental observation, that is, {100} is the preferential cleavage plane in bcc transition metals. In addition, dislocation emissions from the crack front were analyzed; the result supported the notion that plasticity in the vicinity of the crack front determines the preferential cleavage plane.

Characterizing delamination toughness of laminated composites containing carbon nanotubes: Experimental study and stochastic multi-scale modeling

The influence of adding carbon nanotubes (CNTs) to matrix on the delamination resistance of laminated composites is evaluated experimentally and theoretically. A proper multi-scale modeling technique is developed for estimating the interlaminar fracture toughness of laminated composites containing CNTs. Therefore, all involved scales and corresponding parameters are taken into account. Non-bonded interaction is considered between CNT and polymer using adapted cohesive laws resembling CNT-polymer adhesion. The developed modeling is implemented stochastically to take into account the manufacturing-induced inconsistencies. CNT lengths, agglomeration, waviness patterns and orientations are all treated as random variables and thus a full stochastic multi-scale modeling procedure is conducted. Laminated composites with uni-directional glass fibers and epoxy resin reinforced with different portions of CNTs are fabricated for experimental analysis. The specimens are subjected to Mode-I loading and the delamination toughness of the specimens is measured. Considerable improvements are observed due to incorporating CNT as a novel technique to increase the delamination resistance of laminated composites. The outputs of the modeling procedure are in a very good agreement with conducted experimental study.

Study on translaminar fracture toughness under mixed mode I/II load for (0/45)° orientation unidirectional glass/epoxy composite

Mixed-mode translaminar fracture toughness behaviour is experimentally investigated using glass/epoxy composite laminate with (0/45)° orientation. Experimental investigation is conducted using Compact Tension Shear (CTS) mixed mode (I/II) fracture specimens having a/W = 0.5. The specimen plates of thickness 4.5 mm were carefully fabricated using hand lay-up technique. The experiments were conducted for seven loading angles varying from 0° (Mode-I) to 90° (Mode-II) with an increment of 15°. The translaminar fracture toughness and energy release rates were estimated for various loading angles based on the peak loads obtained by experiments. The results indicates that the energy release rate of glass/epoxy composite considered in the analysis is more in pure Mode-I loading than pure Mode-II loading, whereas mixed mode (I/II) loading conditions are in between.

Fracture toughness analysis of HCCD specimens of Longmaxi shale subjected to mixed mode I-II loading

Longmaxi shale exhibits strong anisotropy due to its bedding planes induced by diagenesis. The anisotropic properties of shale have a significant effect on the stability control of geotechnical engineering. To investigate the influence of anisotropy of shale on its mixed mode fracture toughness, we performed Brazilian disc splitting tests on hollow center cracked disc shale specimens with different bedding and crack inclination angles (α and β, respectively). In this study, the fracture toughness of Longmaxi shale was calculated by the finite element method combined with either the J-integral or crack tip-opening displacement method. The results show that the dimensionless stress intensity factors and β values for pure mode-I and mode-II fractures both show anisotropic behavior by varying α. For all combinations of mode-I and mode-II loading, the fracture toughness also exhibits anisotropy by varying α; the mode-I fracture toughness decreases with increasing α when β > 30°, and the anisotropy is negligible for β = 0°. The anisotropy for mode-II fracture toughness is weak when β is small or large, whereas the anisotropy is significant when β = 45° and 60°. The effect of α on mode-I fracture toughness is greater than that on mode-II fracture toughness when β is small or large. Further, a comparison of four mixed-mode fracture criteria with the experimental results shows that the maximum tangential stress criterion for a transversely isotropic body can predict the mixed-mode fracture behavior of Longmaxi shale well. At the same time, it is suggested that the role of the T-stress should be considered to obtain more accurate prediction results.

Investigation of plastic zone dimension in front of an external semi-elliptic crack on pipe of molecular bushing

In automotive industry, molecular bushings transfer loads from steering gearbox to wheels on a vehicle. The pipe is one of the most vital member of these routing systems and manufactured using 41Cr4 sheet metal. For a pipe of molecular bushing, analytical solutions of crack tip plastic zone size is derived by using four yield criteria: Von Mises, Tresca, Hill48, and Hu2003. Hill48 and Hu2003 are useful criteria for materials with higher anisotropy such as sheet metals. Material’s hardening behaviour is modelled using bilinear isotropic hardening rule by coupling with associated flow rule under isotropic and large scale plasticity condition. The solutions are developed for mode-I loading case due to service conditions of the pipe. A finite element simulation is performed to collect stress intensity factors. Results are verified by comparing to those of Irwin and Dugdale. The plastic zone’s shape and size are analysed for different anisotropy cases. The results show that plastic zone have “kidney” or “butterfly” shapes depending on the yield criteria used. Increasing anisotropy has significant effect on plastic zone.

Experimental measurement of mode-I fracture toughness of dissimilar material joints with thermal residual stresses

The current study presents a novel test method to experimentally cancel out the thermal stresses in dissimilar material joints. For the commonly used double cantilever beam test the presence of thermal stresses results in a significant mode mixity at the crack tip, which varies with applied load even if the elastic properties of the adherends are similar. This is particularly a challenge for fibre reinforced plastics bonded to metals due to the large difference in thermal expansion coefficients. The presence of mode-II loading is likely to provide a higher fracture energy from experiments than if tested under pure mode-I loading, which can lead to non-conservative results when using standard test methods. To overcome this challenge a novel test method inspired by the mixed mode bending test is developed. It is shown that the thermal stresses can be cancelled by applying initial constant loads during testing, and that the fracture toughness under pure mode-I loading can be obtained under specific conditions. The test method is validated by carrying out virtual compliance calibration experiments using cohesive zone finite element modelling. As the test method relies solely on analytical calculations and can be used with standard test equipment, it is relatively simple to apply in practice.

A computational framework for predicting the fracture toughness of metals as function of microstructure

We present a simplified computational framework based on the cohesive finite element method (CFEM) for predicting the macroscale fracture measures such as KIC and JIC of ductile metals as functions of microstructural attributes. Currently, no systematic approach exists to explicitly quantify the effects of grain and grain boundary behavior on the fracture measures of polycrystalline materials. Our computational approach involves embedding a microstructure region around the crack tip in a compact tension specimen subjected to mode-I loading and explicitly resolving fracture processes in the microstructure. To track how the interplay between intergranular and transgranular fracture mechanisms affect the fracture processes and consequently KIC and JIC, a grain boundary misorientation dependent interfacial separation model is used. The framework allows exploration of the effects of microstructure on the macroscopic fracture measures via the manifestation of different fracture mechanisms. Calculations carried out for Mo capture and delineate the competing effects between (a) intergranular and transgranular fracture and (b) constituent plasticity and fracture on the overall fracture toughness of the material. The use of statistically equivalent microstructure sample sets (SEMSS) allows the statistical distributions of KIC to be predicted for Mo with different grain sizes. The results indicate that, as the minimum grain boundary interfacial strength decreases and the grain yield strength increases, intergranular fracture becomes more pronounced over transgranular fracture. Consequently, the plastic dissipation primarily associated with transgranular fracture is suppressed, resulting in lower overall fracture toughness. Microstructures with intermediate levels of grain size exhibit the toughest material response via a combination of tortuous crack paths and plastic dissipation. Finally, the results are analytically quantified in a manner that takes into account the effects of grain boundary characteristics, constituent plasticity, and stochasticity via the use of the SEMSS. Although the calculations here are performed on Mo in a simplified setting, the approach can be extended and applied to other material systems.

Effect of texture on crack initiation toughness and the corresponding anisotropy in ductile fracture resistance of thin Zircaloy-4 sheets of Indian PHWR core component

Zirconium alloy core components of nuclear reactors are manufactured following a series of cold-working and heat treatment processes which alter the orientation of grains and hence, their mechanical and fracture properties. Due to the hexagonally close-packed nature of crystal lattice in these alloys, the plastic deformation and the corresponding development of crack-tip constraint is dependent upon the orientation of grains and the major texture. In this work, a thin sheet of Zircaloy-4 has been used to fabricate deeply-cracked compact tension specimens with initial cracks orientated along the rolling and transverse directions respectively. The fracture specimens have been tested at 25 and 300 deg. C, which is the operating temperature of pressurized heavy water type reactors. The crack initiation toughness values have been measured through a modified blunting line expression as well as through measurement of width of stretched zone prior to stable crack growth from scanning electron microscope images. The values of crack initiation toughness as measured through the later method is lower compared to the former signifying physical initiation of crack unlike the approximation associated with 0.2 mm offset line. In addition, the initiation toughness as well as the fracture resistance for specimens with cracks oriented along the rolling direction of the strip are higher when compared to corresponding data for specimens with cracks oriented along the transverse direction. These differences have been explained from point of view of orientation of grains along the rolling direction during the fabrication process of these sheets. The grains plastically deform easily for loading along the transverse direction which is the mode-I loading direction for cracks oriented along rolling direction. The associated loss of crack-tip constraint raises the fracture resistance for rolling direction cracks.

Underlying fracture trends on Mode-I crack multiple-branching

An energy-based modelling has been proposed to capture the physical process of multiple cracks initiation from a Mode-I crack tip. The underlying fracture trends and instability on crack tri-branching, symmetric branching and side-branching induced by dominant Mode-I loading are formulized. The solutions of the energy release rate, crack initiation angles and K-based fracture criterion for multiple cracks initiation have been investigated. The upper limit on the number of possible crack initiation is given for a Mode-I crack. The discussions in present article indicate that some underlying fracture configurations for Mode-I crack can be triggered by using impulse loading. Many fracture behaviours for a Mode-I crack can be better explained and understanding based on the present theoretical modelling. The fracture toughness predicted by the present modelling and Griffith’s criterion agree well with experimental results.

Inter-granular fracture toughness of bi-crystalline graphene nanosheets

Aim of this research article was to study inter-granular fracture toughness of graphene containing edge crack. Molecular dynamics based simulations were performed in conjunction with AIREBO potential to study the crack tip behaviour in pristine and bi-crystalline graphene nanosheets. Higher value of linear dislocation density at the grain boundaries helps in improving the fracture toughness of bi-crystalline graphene, and trend was predicted to be independent of chirality vector in mode-I loading. Higher dislocation density imparts lower change in critical bond length with applied strain, which helps in improving resistance to crack growth. Additionally, switching between heptagon and pentagon rings positioning at the crack tip also helps in improving the fracture toughness of bi-crystalline graphene. Crack tip containing heptagon rings has positive effect on the fracture toughness of bi-crystalline graphene as compared to pentagon rings. Outcome of the analysis will provide new insights in fracture properties of bi-crystalline graphene that further helps in utilising graphene nanosheets in mechanically robust applications such as pressure barrier, nanocomposites and ion-separation.

An asymptotic finite plane deformation analysis of the elastostatic fields at a crack tip in the framework of hyperelastic, isotropic, and nearly incompressible neo-Hookean materials under mode-I loading

In this work, stress and displacement fields were computed around a crack tip in the case of nearly incompressible and isotropic neo-Hookean material. The constitutive equation was linearized, so that the Cauchy stress tensor could be written as a sum of two components: the linear response in term of elastic Hooke’s law and the nonlinear one. Based on this decomposition, an asymptotic analysis has been developed, the fields of linear elastic fracture mechanics (LEFM-theory) are the zero-order terms of the asymptotic expansion. The validity of the proposed theory has been checked in the case of a mode-I crack problem. A numerical model was constructed using a finite element method. It has shown that the computed fields arising from this theory are qualitatively in agreement with those of the finite element simulations.