Mixed Mode Fracture Resistance Research Articles

A strain-based criterion for predicting size-dependent fracture resistance of quasi-brittle materials under mixed mode loading

In the present study, a strain-based approach called the modified maximum tangential strain criterion has been developed for evaluating size effect on the mixed-mode fracture resistance of quasi-brittle materials. This approach relies on the generalized maximum tangential strain criterion, which considers the singular (K) and the first non-singular (T) terms of Williams series expansion. Furthermore, as an important and size-dependent parameter in the proposed criterion, a new formulation is presented to calculate the critical distance (rc). The predictions of the new criterion are compared not only with the available experimental data, but also with the results estimated by another size effect criterion named the modified maximum tangential stress criterion. It is shown that the proposed strain-based criterion is highly capable of estimating the size-dependent mixed-mode fracture behavior of quasi-brittle materials without requiring to compute the other higher order terms.

J integral strain-curvature approach for multilayer fracture specimens with unknown thickness and stiffness of layers

In the coming years, many wind turbines will reach their planned design life, and it is of great interest to investigate if their service life can be extended so that the turbines can produce a larger amount of electricity before decommissioning. Such an assessment can include the measurement of the fracture mechanics properties of materials interfaces, e.g., for trailing edge bondlines, web foot bondlines and interfaces between layers in the load-carrying main spars. It would then be preferable to conduct the fracture mechanics testing and data analysis by approaches that give accurate results with the smallest amount of testing. In the present work we propose an approach for measurement of mixed mode fracture resistance (and mixed cohesive laws) that does not require knowledge of the stiffness properties and the elastic centre of the laminates of the test specimens. This is advantageous since the layer stiffness, layer thickness and the lay-up of a laminate cut from an old blade may not be known. Furthermore, the elastic properties of polymer resins of bondlines and matrix materials in fibre composites can have changed (aging) due to the blades long-time environmental exposure.

The impact of sterilization, body environment condition and raster orientation on tensile-shear cracking of sub-sized 3D printed specimens

Use of 3D printed parts in biomedical applications has received attention recently. The applied loads, manufacturing pre-processing factors or in vivo conditions may affect the reliability and integrity of such implants. To obtain deeper understand regarding the cracking resistance and microstructure of extrusion-based 3D printed acrylonitrile butadiene styrene (ABS) material a number of sub-sized and short bend beam samples are manufactured. The influence of raster orientation, Gamma radiation sterilization, body environment (saline 0.9% at temperature of 37 °C) and combined Sterilized process & body environment was studied on the mixed-mode I + II fracture toughness and strain energy release rate values. It was observed that exposing the 3D printed ABS material to Gamma-radiation process can increase noticeably the mixed mode fracture resistance compared to the control sample. Printing pattern with raster orientation of ±45° provided a higher mixed-mode fracture envelope compared to pattern of 0/90° for all investigated environments. The microstructure study of SEM pictures obtained from the investigated samples showed dominantly ductile type fracture with some evidences such as formation of dimples and ridge markings. The depth and number of ridge markings and dimples were increased by moving towards mode II (shear mode loading) and for the samples exposed to body environment.

A semi-analytical method for determining the mixed mode I/II fracture resistance and mode mixture of ADCB laminates

The crack tip of the asymmetric double cantilever beam (ADCB) under mode-I loading is often accompanied by a proportion of mode II component, thus it is a typical mixed-mode I/II problem. Characterizing the mixed-mode I/II fracture resistance behavior and mode partition in ADCB laminates is of great significance for studying the mode mixture phenomenon. In this work, a semi-analytical method is proposed to determine the mixed-mode fracture resistance curve (R-curve) and mode mixture of ADCB composite laminates. Considering the use of the equivalent crack length related to compliance, the global crack growth rate ratio correction model is proposed. The results derived from the proposed semi-analytical method is compared with other theoretical methods to verify its effectiveness and wide applicability for ADCB laminates with various material systems and stacking sequences. In contrast, the semi-analytical method with the global crack growth rate ratio correction requires fewer measurement data and gives accurate R-curve results. In addition, it makes the mode partition during the whole delamination growth process with physical meaning.

Mixed-mode fracture prediction of acrylonitrile butadiene styrene material fabricated via fused deposition modeling

Fused deposition modeling is one of the additive manufacturing techniques that is used for rapid manufacturing and prototyping, in various industries. Due to the layer-wise fabrication routine in the fused deposition modeling process, the final fabricated products often show anisotropic behavior. As a result, to investigate the mechanical performance of the three-dimensional-printed parts, complex and time-consuming analyses are required. The main purpose of the current research paper is to determine whether the isotropic assumption of material using maximum tangential stress and mean stress criteria is capable of predicting the mixed-mode fracture resistance of the three-dimensional -printed parts. Here, three different building conditions are considered for fabricating tensile and fracture specimens, and various mechanical and fracture characteristics are evaluated. Finite element simulations of the test specimens are executed and the stress results are used as input for fracture prediction of the fused deposition modeling parts. Two different cases are considered for isotropic assumptions wherein the first case (case A), each fracture specimen is modeled by using its own direct mechanical properties. While in the second case (case B), the average mechanical properties are used for modeling the cracked specimens. The results showed that both maximum tangential stress and mean stress criteria can predict the fracture loads of the fused deposition modeling parts, without the need for complex and time-consuming analyses associated with fully anisotropic materials. In addition, an improvement of the predictions was observed while using case A compared to case B.

Investigation of the deleterious effects of low-temperature and hygrothermal aging conditions on the mixed-mode fracture resistance of epoxy resin using a short-beam bend specimen

The effect of different environmental aging conditions on the mixed-mode fracture behavior of epoxy resins was investigated using a sub-size specimen. The short-beam bend (SBB) specimens with different crack inclination angles were manufactured and subjected to low-temperature (-71 °C), hygrothermal (immersion in deionized water at 60 °C) and room-temperature conditions. The deleterious effect of low-temperature and hygrothermal aging conditions on the mode-I, mode-II and mixed-mode I/II fracture responses of the epoxy resin was studied by testing the aged and unaged SBB specimens under three-point bend loading. The experimental results indicated that the hygrothermal aging condition, with a reduction of 49% in the effective fracture toughness, imposed a more severe deleterious effect on the fracture response of the specimens in comparison with the low-temperature condition with a decrease of 35% in the effective fracture toughness. The generalized maximum tangential stress criterion was used to predict the fracture loads of the aged and unaged specimens. Moreover, optical microscopy and scanning electron microscopy techniques were employed to assess the fracture surfaces of the specimens aged under different conditions.

A stress-based approach for considering the size effect on the mixed mode fracture behavior of rock

It is aimed in this research that a new approach is represented for justifying the influence of specimen size on the mixed mode I/II fracture behavior of rock. The new approach, namely, the MTS-FEM criterion, is an extension of the maximum tangential stress (MTS) criterion in which the finite element method (FEM) is employed for characterizing the tangential stress at the critical distance. Also, two points exist in the MTS-FEM approach for the critical distance. First one is that the critical distance is obtained directly from finite element analysis corresponding to results of mode I fracture test. The second point is that the critical distance from the crack tip is considered as a function of specimen size. The experimental results carried out in the previous studies on cracked Brazilian disks (CBD) with four different radii and under mixed mode loading are utilized with the aim to evaluate the new size effect criterion. It is illustrated that the MTS-FEM criterion is able to predict the mixed mode fracture resistance of rock considering the size effect well without calculating any parameters related to the stress or strain series expansion.

Experimental study on the quasi-static loading rate dependency of mixed-mode I/II fractures for marble rocks

To explore the quasi-static loading rate effect on the mixed-mode I/II fractures of rock materials, the centrally cracked Brazilian disc (CCBD) specimens prepared from a marble rock were tested under different mixed-mode loading conditions (Me = 0, 1/3, 2/3, and 1) and quasi-static loading rates (0.05 mm·min−1, 0.1 mm·min−1, 0.5 mm·min−1, and 5 mm·min−1), and the generalized maximum tangential strain energy density (GMTSED) criterion was also derived to discuss the development of mixed-mode fracture toughness and crack initiation angle. Based on the experimental and analytical results, several conclusions were obtained. (1) The mixed-mode fracture toughness gradually increases with increasing the quasi-static loading rate, while the crack initiation angle and fracture geometry of the tested specimens change barely; the specimen might have a higher rate dependency of the fracture toughness under mode I dominant loading. (2) The modified criteria (GMTSED, EMTSN, and GMTS) match well with the experimental results; the theoretical predictions based on GMTSED criterion is between the predictions of the EMTSN and GMTS criteria. (3) The critical distance of the tested rock is not sensitive to the quasi-static loading rate, which means that the fracture behavior, i.e. crack initiation angle and mixed-mode fracture resistance, under quasi-static high loading rate can be well predicted by only taking into account the critical distance obtained at quasi-static low loading rate.

Mixed-mode crack growth simulation in aviation engine compressor disk

This study focuses on a mixed mode crack growth analysis of an aviation gas turbine engine (GTE) compressor disk based on simulation principles. The operation damages occur via inclined surface cracks in a “dovetail type” disk-and-blade attachment. Based on the sizes and configuration of this attachment, three geometries for simulation models of the GTE compressor disk are proposed. The biaxial loading conditions of the simulation models are determined and numerically verified to reproduce the stress-strain state in critical zones of the compressor disk during operation. To determine the elastic-plastic fracture mechanical parameters, a 3D full-size finite element method (FEM) analysis is conducted for the GTE compressor disk and simulation models, based on operating loading conditions. As a result, the distributions of the new mixed-mode fracture resistance parameters in the form of equivalent elastic and plastic stress intensity factors along the crack front in the disk-and-blade dovetail-type attachment are applied to the experimental uniaxial and biaxial data for crack growth rate interpretation. The possibility of using the proposed simulation principles for an assessment of the structural integrity of GTE rotating disks is discussed.

Influence of basalt fiber on mode I and II fracture properties of asphalt mixture at medium and low temperatures

Basalt fiber could effectively improve the crack resistance of asphalt mixture. However, most cracks in asphalt pavement present complex fracture characteristics. Effect of basalt fiber on the mixed mode fracture resistance of asphalt mixture is still unknown. Thus, the asymmetric semi-circular bend test was used to study the mode I and II fracture properties of the control and basalt fiber reinforced asphalt mixtures (BFRAM) at low and medium temperatures. Influences of basalt fiber on the critical stress intensity factor and critical fracture energy of asphalt mixture were investigated. The applicability of different fracture criterions to asphalt mixture also was discussed. Results indicate that the critical stress intensity factors of BFRAM first decreases and then increases with the rise of Me (which describes different fracture modes) at medium and low temperatures. Basalt fiber soundly improves the critical fracture energy of asphalt mixture at medium and low temperature even though it reduces the critical stress intensity factor at 20 ℃. The reinforcing effect of basalt fiber is optimal for the mixed mode fracture. Generalized maximum tangential stress (GMTS) criterion is suitable for the prediction of fracture initiation angle. The linear empirical fracture criterion has good applicability to the control and basalt fiber reinforced asphalt mixtures. This work can be used to analyze the mixed modes fracture of asphalt layers.

Numerical investigation on dynamic fracture behavior of cracked rocks under mixed mode I/II loading

Research on rock fracture behavior is usually limited to static mixed mode I/II fracture and static or dynamic mode I fracture. In this study, the notched semi-circular bend (NSCB) specimens with different notch inclination angles were introduced into the split Hopkinson pressure bar (SHPB) system to numerically investigate dynamic mixed mode I/II fracture behavior of cracked rocks. First, the feasibility and reliability of our discrete-element-method-based numerical system to model dynamic fracture behavior of rock were validated; then, the effects of different mixed mode loading conditions and various loading rates on the mixed mode fracture of NSCB specimens were studied. The dynamic mixed mode fracture of the specimens was found to be mainly induced by tensile damages at the micro scale. The results also showed the loading rate dependence of the mixed mode fracture resistance. Moreover, for the same increment of the loading rate, the dynamic mode I fracture toughness increases more than the dynamic mode II fracture toughness. Subsequently, the fracture resistance and fracture initiation angles observed in the modeling were compared with the theoretical predictions based on some brittle fracture criteria. It was demonstrated that a semi-analytical criterion could reproduce well the dynamic mixed mode fracture behavior of rocks.

Experimental and theoretical fracture assessment of rock-type U-notched specimens under mixed mode I/II loading

The aim of this paper is to present a new approach for predicting the mixed-mode fracture resistance of rock-type specimens containing U-shaped notches. The new approach is a modified form of maximum tangential stress (MTS) criterion which states the fracture takes place when the maximum tangential stress at the critical distance from the notch border attains critical value. The critical distance in rock-type specimen is relatively large and the formulations presented in the conventional MTS for characterizing the tangential stress component cannot provide good estimates. Therefore, the modified MTS (MTS-FEM) criterion proposes that the value of maximum tangential stress at the critical distance is determined directly from finite element analysis. Several mixed-mode fracture tests were conducted on the Brazilian disks weakened by central U notches in order to evaluate the MTS-FEM criterion. The comparison between the fracture loads obtained from experiments and those predicted by the MTS-FEM criterion shows that the MTS-FEM criterion can provide good estimates for fracture loads of rock-type U-notched samples under mixed mode loading.

The mixed-mode fracture resistance of C 50/60 and its suitability for use in precast elements as determined by the Brazilian disc test and three-point bending specimens

The mixed mode fracture behaviour of C 50/60 concrete was studied both experimentally and theoretically using two different test configurations (three-point bending and Brazilian disc tests with various crack lengths). Different fracture behaviour in mode I was observed for the tested specimens. The level of crack tip constraint in the test-specimens (which relates to the stress intensity factors (SIF or K) and the T-stress) was used as the main parameter for predicting the mixed mode fracture results based on a two parameter (K-T) linear elastic fracture theory. To predict the crack initiation angles and fracture resistances, the generalized maximum tangential stress (GMTS) criterion was employed. The GMTS simultaneously involves the effects of the mixed mode SIFs, the T-stress and a critical distance rC. For each test configuration, a fracture initiation direction, a fracture toughness and mixed mode fracture resistance curves were obtained throughout the entire range of the mixed mode I/II loading conditions. It was observed that for all specimens the loss of the crack tip constraint increases the mixed mode fracture resistance and decreases the fracture initiation direction and vice versa.

Fracture and microstructural study of bovine bone under mixed mode I/II loading

Understanding the fracture behavior and associated crack growth mechanism in bone material is an important issue for biomechanics and biomaterial researches. Fracture of bone often takes place due to complex loading conditions which result in combined tensile-shear (i.e. mixed mode) fracture mechanism. Several parameters such as loading type, applied loading direction relative to the bone axis, loading rate, age and etc., may affect the mixed mode fracture resistance and damage mechanism in such materials. In this research, a number of mixed mode I/II fracture experiments are conducted on bovine femur bone using a sub-sized test configuration called “compact beam bend (CBB)” specimen to investigate the fracture toughness of bone under different mode mixities. The specimen is rectangular beam containing a mid-edge crack that is loaded by a conventional three-point bend fixture. The results showed the dependency of bone fracture toughness on the state of mode mixity. The fracture surfaces of broken CBB specimens under different loading conditions were studied via scanning electron microscopy (SEM) observations. Fracture surface of all investigated cases (i.e. pure mode I, pure mode II and mixed mode I/II) exhibited smooth patterns demonstrating brittle fracture of bovine femur. The higher density of vascular channels and micro-cracks initiated in the weakened area surrounded by secondary osteons were found to be the main cause of the decreased bone resistance against crack growth and brittle fracture.

Fracture toughness of rough and frictional cracks emanating from a re-entrant corner

In mixed-mode conditions, the competing contribution of the different stress intensity factors predicts fracture initiation load as well as crack propagation direction. Commonly, mixed-mode fracture resistance is based on the assumption of smooth and frictionless cracks. However, the effect of friction and roughness cannot be neglected when mixed mode loading occurs, as in the case of a crack emanating from a re-entrant corner. In this paper, the effect of friction and roughness is evaluated through a simple saw-tooth model in a three-quarter-infinite plane (corresponding to a 90 degree re-entrant corner). The crack surfaces are assumed to be globally smooth, and roughness and friction are incorporated through a constitutive law between opposite crack surfaces. The solution is found using the distributed dislocation method, and an iterative algorithm is needed due to the non-linearity of the model. The effect of friction and roughness angle is discussed for a simple case.

Mixed mode fracture analysis of CCBD specimens based on the extended maximum tangential strain criterion

AbstractThe maximum tangential strain (MTSN) criterion has been modified to include the effects of T‐stress and stress intensity factors in conditions of both plane stress and plane strain. Further, both the T‐stress and Poisson's ratio affecting the crack propagation are also discussed according to the extended MTSN (EMTSN) criterion, which is a modified MTSN criterion. Finally, the generalized maximum tangential stress (GMTS) criterion and the EMTSN criterion are used to predict the test results obtained with central cracked Brazilian disc (CCBD) specimens. The results indicate that the T‐stress and Poisson's ratio have a remarkable influence on the mixed mode fracture resistance based on the EMTSN criterion. Theoretical values of both the EMTSN and the GMTS criteria are in very good agreement with the test results. Moreover, the EMTSN criterion provides a better prediction for pure mode II.

Mixed mode fracture analysis using generalized averaged strain energy density criterion for linear elastic materials

A modified energy-based model called the generalized averaged strain energy density (ASED) criterion is proposed to predict the mixed mode I/II fracture resistance of brittle and quasi-brittle materials. The proposed criterion takes into account the effect of T-stress in addition to the stress intensity factors KI and KII when calculating the strain energy density averaged in a control volume around the crack tip. The effect of T-stress on the mixed mode fracture resistance of materials is investigated by using the generalized ASED criterion and the generalized SED criterion. The results predicted by these criteria are compared with the experimental results reported in the literature from fracture tests conducted on the Brazilian disc specimens and the semi-circular bend specimens made of Harsin marble and Guiting limestone. It is shown that the theoretical estimates of the generalized ASED criterion are consistent very well with the experimental results. The theoretical results also show that the specimens having a negative T-stress require higher loads in order their averaged strain energy density around the crack tip attains its critical value.

A 3D two-scale multiplane cohesive-zone model for mixed-mode fracture with finite dilation

A 3D multi-scale cohesive-zone model (CZM) combining friction and finite dilation by a multi-plane approach (M-CZM), based on the concept of Representative Multiplane Element (RME), is developed within the mechanics of generalized continua for the analysis of mixed-mode fracture.The proposed M-CZM formulation captures the increase of measured fracture energy in mode II as a natural effect of multi-scale coupling between cohesion, friction and interlocking, employing a reduced set of micromechanical parameters characterized by a well-defined micromechanical interpretation. This permits to devise clear calibration and identification procedures for 3D fracture problems.Upon assessing the retrieval, by a regular 5-plane RME, of a quasi-isotropic response for fracture resistance and for dilation, the M-CZM is employed in FEM simulations of Double-Cantilever Beam (DCB) tests to obtain predictions of mixed mode I–II and mixed mode I–III fracture resistance.The DCB analyses show the key role of the characteristic height of asperities in determining the macroscopic fracture resistance in both mixed mode I–II and I–III interactions. Numerical results also show the independence of the mode-I fracture resistance on the geometry of the beam section and a marked dependence of the measured mixed-mode fracture resistance on the section aspect ratio.

Local strain energy density to predict size-dependent brittle fracture of cracked specimens under mixed mode loading

In this paper the SED-approach is applied to a set of experimental data reported in the literature. Data are referred to mixed mode fracture resistance of Guiting Limestone, a sedimentary soft rock. Two types of specimens have been investigated: cracked Brazilian disk (BD) specimens under diametral compression and edge cracked semicircular bend (SCB) specimens under three-point bend loading. To evaluate size dependent behavior, specimens characterized by four different radii were tested under different mode mixities.To assess the static strength of cracked components the strain energy density (SED) criterion has been used. It is shown that this criterion can predict the size-dependent fracture behavior of Guiting Limestone. Critical experimental loads have been compared with the theoretical ones, estimated keeping constant the critical value of strain energy density (SED). The dimension of the control volume was found to be a function of specimen size and geometry.

Size effects on mixed-mode fracture behavior of polygranular graphite

The aim of this paper is to present a combined experimental-theoretical approach for studying the effects of specimen size on the mixed mode fracture resistance of a polygranular graphite. The edge cracked semi-circular bend (SCB) specimens under three-point flexural loading with different sizes are used for conducting the fracture tests on graphite. The experimental results revealed that the fracture resistance of graphite increases significantly with specimen size. For instance, the effective fracture resistance in pure mode I loading enhances from 0.585 MPa√m to 1.115 MPa√m when the sample radius increases from 5 mm to 30 mm. To justify the size effect on the fracture resistance of graphite, the modified maximum tangential stress (MMTS) criterion is employed. The criterion makes use of a more accurate mathematical model for calculating the stress field around the crack tip. The MMTS criterion also assumes that the extent of fracture process zone around the crack tip depends on the size of specimen. It is shown that the MMTS criterion can provide good estimates for the fracture resistance of graphite samples and hence it can be used for predicting the fracture loads of real graphite components with different sizes.