Mixed Mode Loading Research Articles

Simulating delamination growth accounting for fracture directionality using a cohesive element approach

Experiments have shown that the critical energy release rate (ERR) can vary as a function of the delamination in-plane propagation direction, relative to the bounding plies, and out-of-plane direction towards which it tends to grow, often referred to as delamination directionality. Despite the experimental evidence, delamination directionality is typically neglected in simulations. A cohesive element formulation is proposed that can simulate delamination growth while accounting for delamination directionality. The simulated fracture process is defined via piecewise-linear, independent, Mode I, II, and III traction separation laws (TSLs) and a directional mixed-mode fracture criterion. Mixed-mode loading conditions are simulated by scaling the pure mode TSLs based on the fracture criterion and the calculated mode-mixity. The same scaling concept is used in partially damaged material points to ensure that a change in fracture process (e.g. decrease/increase in critical ERR due to a variation in delamination directionality) is captured while preventing spurious delamination growth or healing and minimizing history dependence.

Experimental Study on Shear-Peeling Debonding Behavior of BFRP Sheet-to-Steel Interfaces.

In order to study the failure mode and debonding behavior of the interface between BFRP (basalt fiber reinforced polymer) sheet and structural steel under mixed-mode loading conditions, eighteen specimens with different initial angles were tested in this study. The specimens were designed with different initial angles to ensure that the interface performed under mixed-mode loading conditions. The relations between the bond strengths, failure modes, and initial angles were investigated. A new evaluation method to predict the interfacial bond strength under shear-peeling loading mode was proposed. The test results show that specimens with a smaller initial angle are more likely to exhibit a shear debonding failure at the interface between the steel plate and adhesive. In contrast, specimens with a larger initial angle are more likely to exhibit peeling of the interface. The ultimate tensile strength of the specimen is higher with a smaller initial angle. The results predicted by the proposed method are in good agreement with the experimental results.

Role of composition in fracture behavior of two-phase solids.

In a two-phase solid, we examine the growth of a preexisting macroscopic crack based on simulations of a random spring network model. We find that the enhancement in toughness, as well as strength, is strongly dependent on the ratio of elastic moduli as well as on the relative proportion of the phases. We find that the mechanism that leads to enhancement in toughness is not the same as that for enhancement in strength; however, the overall enhancement is similar in mode I and mixed-mode loading. Based on the crack paths, and the spread of the fracture process zone, we identify the type of fracture to transition from nucleation type, for close to single-phase compositions, whether hard or soft, to avalanche type for more mixed compositions. We also show that the associated avalanche distributions exhibit power-law statistics with different exponents for each phase. The significance of variations in the avalanche exponents with the relative proportion of phases and possible connections to the fracture types are discussed in detail.

Experimental study and hybrid optimization of material extrusion process parameters for enhancement of fracture resistance of biodegradable nanocomposites

Among the additive manufacturing processes, the material extrusion (ME) is the most popular and affordable technique in production of a wide range of products, from prototypes to the final products, for different industrial sectors. The most popular raw material in this process is the biodegradable polylactic acid (PLA) polymer that offers ease of production in relatively low price and wide applications in synthesis of medical proteases. However, the mechanical strength of fabricated samples and their resistance against the fracture loadings, which are critical for components synthesized for medical applications, are strongly dependent on the ME process parameters and the composition of the base material. Therefore, this study is aimed to address both the strengthening mechanisms of inorganic CaCO3 nanoadditives in the PLA matrix and the influence of ME process parameters on the fracture resistance of fabricated samples. To this aim, the PLA/CaCO3 nanocomposite filaments have been produced by mix-blending/extrusion technique and were employed to fabricate tensile and fracture test samples in ME process under different sets of parameters, including printing speed, layer thickness, filling ratio and printing pattern, determined by Taguchi L27 orthogonal array. The fracture experiments were conducted on a uniaxial tensile test machine using a specially designed fixture that makes the application of mixed-mode loading on fracture samples possible. The results of fracture toughness of specimens were employed as input data to model the response of fabricated samples and to determine the ME parameter levels and nanoparticle concentrations for maximum fracture resistance of fabricated samples based on a hybrid algorithm of artificial neural network and ant colony optimization (ANN/ACO). Differential scanning calorimetry was used to characterize the thermal features (i.e. glass transition, crystallization and melting temperatures) as well as the degree of crystallization of ME samples. Scanning electron microscopy of fracture surfaces were employed to study the influence of ME parameters and CaCO3 nanoadditives on the characteristics of fracture of 3D printed specimens under various modes of loading. Overall, the results showed that the effects of ME parameters on the fracture behavior of 3D printed samples are highly interconnected and, in the case of a semicrystalline polymer, are highly dependent on the physical characteristics of the fabrication process, including the heat transfer and crystallization rate of the matrix.

Study on mixed-mode fracture behavior of TC4 titanium alloy

Mixed mode fracture behaviors of TC4 titanium alloy are studied by finite element method, testing and theoretical analysis systematically. Results show that there exists II-III coupling effect ahead of crack tip for mixed mode crack, based on which three-dimensional stress intensity factors are defined and calculated; The crack under I-II mixed mode loading exhibits a planar propagation state, the deflection angle increases with mode II component increasing; I-II mixed mode fracture of TC4 shows the characterization of brittle fracture mechanism, and brittle fracture criteria are in agreement with test results with some conservative. While the crack under I-III mixed mode loading exhibits a spatial propagation state, the deflection angle firstly increases then decreases with mode III component increasing; It is due to that the fracture mechanism is from brittle to brittle-ductile mixed fracture mode, as mode III component increases. The brittle criterion has a good prediction on I-III mixed mode brittle fracture behavior, with mode III component lower enough. The conclusions in this paper are of great significance to the mixed mode fracture evaluation of TC4 titanium alloys.

Mixed-mode fracture analysis of FGMs using [formula omitted]-integral: Formulation and FE implementation

This paper introduces a computational method based on the Jk-integral for mixed-mode fracture analysis of isotropic functionally graded materials (FGMs), subjected to mixed-mode loading. The present development is implemented by means of the finite element method (FEM), by couplingofAnsys and Matlabsoftware’s. The continuous variations in the material parameters of the functionally graded medium are treated by specifying the material properties at the centroid of each finite element. The Jk-integral implementation is validated numerically by considering two different problems, the edge-cracked FGM plate and the four-point bending specimen with crack parallel to material gradation. The presented results illustrate the influences of material property gradation and crack geometry on the mixed-mode SIFs. The comparisons reported by available reference solutions indicate also that the numerical results obtained by present method have a high precision and that the expanded form of the Jk-integral is independent of the domain.

A Cohesive-Zone-Based Contact Mechanics Analysis of Delamination in Homogeneous and Layered Half-Spaces Subjected to Normal and Shear Surface Tractions

AbstractA contact mechanics analysis of interfacial delamination in elastic and elastic-plastic homogeneous and layered half-spaces due to normal and shear surface tractions induced by indentation and sliding was performed using the finite element method. Surface separation at the delamination interface was controlled by a surface-based cohesive zone constitutive law. The instigation of interfacial delamination was determined by the critical separation distance of interface node pairs in mixed-mode loading based on a damage initiation criterion exemplified by a quadratic relation of the interfacial normal and shear tractions. Stiffness degradation was characterized by a linear relation of the interface cohesive strength and a scalar degradation parameter, which depended on the effective separation distances corresponding to the critical effective cohesive strength and the fully degraded stiffness, defined by a mixed-mode loading critical fracture energy criterion. Numerical solutions of the delamination profiles, the subsurface stress field, and the development of plasticity illuminated the effects of indentation depth and sliding distance on interfacial delamination in half-spaces with different elastic-plastic properties, interfacial cohesive strength, and layer thickness. Simulations yielded insight into the layer and substrate material property mismatch on interfacial delamination. A notable contribution of the present study is the establishment of a computational mechanics methodology for developing plasticity-induced cumulative damage models for multilayered structures.

Accurate simulation of delamination under mixed-mode loading using a multilinear cohesive law

The complex failure mechanisms involved in failure of interfaces requires the use of an accurate description of the cohesive law. In recent years, there have been many developments to determine the full shape of the cohesive law. However, most of the existing cohesive zone models assume a simplified shape, such as bilinear, trapezoidal or exponential, which are usually simple to model. Their accuracy is found to be rather limited, especially in the presence of a large fracture process zone due to either plastic deformation or fibre bridging. In this work, a new cohesive element description is proposed to formulate a general cohesive zone model to overcome these limitations. The benefit of the new approach is that it allows for convenient implementation of any arbitrary shape of the cohesive law obtained experimentally. The authors present a new procedure based on the superposition of n-bilinear cohesive zones to obtain an equivalent multilinear cohesive law that fits any experimental measurement. The new element formulation has been implemented in the commercial finite element software ABAQUS, using user element subroutine. Verification of the methodology is performed at the single element level and the approach is validated for different material systems (adhesives and composites) using the double cantilever beam, end-notched flexure and mixed-mode bending tests. Excellent correlation between all numerical predictions and experimental results is obtained, demonstrating the robustness of the proposed methodology.

Fatigue crack growth behavior of AA2024T3 under mixed mode loading within the framework of EPFM

Fatigue crack growth behavior of AA2024T3 under mixed mode loading within the framework of EPFM

Evolution of the FPZ in steel fiber-reinforced concrete under dynamic mixed-mode loading

This work studies the fracture process zone (FPZ) evolution of steel fiber-reinforced concrete under dynamic mixed-mode loading. We made beams with fiber contents of 0%, 0.4%, and 0.8% in volume and tested them in three-point bending at low displacement rates (2.2 μm/s and 22 mm/s) and impact rates (1.77 m/s and 3.55 m/s). All beams had a notch in the center of the half-span to facilitate a mixed-mode process zone extended from its tip. We recorded the entire crack propagation process in all the tests with a high-speed camera. Using the digital image correlation (DIC) measurements, we locate the FPZ tip from the tensile strain field and determine the stress-free crack tip from the displacement jumps. In this way, we capture the entire process of FPZ evolution. The FPZ stretched with crack propagation until a maximum —full FPZ length— and shortened afterward. The FPZ length at peak load and its maximum value increased with the loading rate. The loading rate and the fiber content have opposite effects on the full FPZ length. The faster the loading rate, the longer the full FPZ length. The more fiber content, the shorter the full FPZ length. In addition, the fiber addition helped to generate multiple FPZs and to cause more distributive damage in the matrix. Under impact loading, the cracked matrix and the steel fibers work in a synergetic way to dissipate the excessive energy input due to impact.

Brittle fracture prediction method considering mixed modes for column-to-beam connections

This study entailed an improvement in fracture assessment based on mixed-mode loading. Brittle fractures can be evaluated using the Weibull stress regardless of the differences in plastic constraints. However, the Weibull stress is proposed for cracks subjected to open loading (mode I), and it does not consider the effects of in-plane (mode II) or out-plane shear loadings (mode III). Structural connections under large deformations are subjected to modes I, II, and III at the crack tip. Fracture tests on beam-to-diaphragm connections in buildings have indicated that failure occurs when ductile cracks propagate from the strain concentration region of a weld access hole, where mode II dominates. Additionally, they cannot be appropriately evaluated using the conventional Weibull stress approach. This study investigated the relationship between mode differences and fracture initiation for several specimens modeled as beam-to-diaphragm connections. A mixed-mode ratio with stress intensity factor was used as an index to evaluate the mode differences. The fracture prediction considers the differences in modes by correcting the evaluated values on the basis of the mixed-mode ratio. The correction results shows more reasonable fracture prediction than conventional methods for beam-to-column connections under different modes.

A novel cohesive zone modelling approach to represent mixed mode loading and bond line thickness effects

ABSTRACT Accurate representation of the traction–separation response for mixed mode loading in a cohesive zone model (CZM) is critical to predicting the response of adhesive joints in a number of applications, including transportation and vehicle crashworthiness. Traditionally, the Mode I and Mode II responses are treated independently, with mixed mode response determined by relationships between the degree of mode mixity and separation, potentially leading to overprediction of the plateau traction and underprediction of the plateau length in mixed mode loading. This poor fit is due to the indirect relationship between mixity and traction and having minimal fitting options for separation-to-plateau and softening. To address this limitation, a mixed mode CZM approach is proposed, based on measured mixed-mode traction–separation results for a toughened epoxy adhesive. The effects of bond-line thickness were considered, to examine the ability of the proposed approach to include additional effects (beyond mode mixity) that are known to affect the traction–separation response. The CZM implementation was assessed using the original test data and was shown to capture the measured experimental traction–separation response across a range of mixed mode loading and bond line thickness more accurately compared to traditional CZM treatments.

Jk-integral applied to mixed-mode fatigue crack propagation and life prediction in metal welding interface

In this paper, an innovative fatigue crack propagation model of metal welding interface is investigated based on the concept of Jk-integral (k = 1, 2) in elastic–plastic material, including the prediction of crack propagation path and life. In order to validate the effectiveness of the present fatigue model, the experiments of mixed-mode interface fatigue cracks are carried out on compact tensile shear specimens of N36 zirconium alloy using DIC methods. The results demonstrate that the fatigue crack only propagates along the interface under mode I loading where the relationship between the crack growth rate da/dN and ΔJ1 (the J1-integral range per loading cycle) is logarithmic linear. As for mode I/II mixed-mode loading, interface cracks start to propagate along the interface when J1 reaches Jint-C (the interface fracture toughness). When Jtotal (the vector sum of J1 and J2) reaches Jsub-C (the substrate fracture toughness), the crack deflects to the substrate in the Jtotal direction. In this case, da/dN shows a two-stage logarithmic linear relation with ΔJtotal (the Jtotal-integral range per loading cycle) under mixed-mode loading, and the critical Jtotal at the beginning of crack deflection is approximately matching the specific value. The theoretical deflection angle (i.e. the Jtotal direction) calculated from the corresponding J1 and J2 at the beginning of crack deflection is wellconsistentwiththe actual deflection angle observed in experiments. Moreover, the model can clearly describe the two-stage process from the crack propagation along the interface to the crack deflection to the substrate under mixed-mode loading. It is concluded that the proposed fatigue model based on Jk-integral can accurately predict the fatigue crack propagation path and lifetime of metal welding interface.

The Impact of Nano-TiO2 Particles on the Moisture Susceptibility and Fracture Toughness of HMA under Mixed-Mode I/II Loading and Various Crack Geometry and Temperatures

In recent decades, some of the main goals of pavement engineers have been to increase bearing capacity, enhance tensile strength, and improve the moisture susceptibility of asphalt mixtures. Because moisture and frost intensify the damage caused by traffic loads on pavements in cold climates, the life and safety of asphalt pavements in this climate are reduced. Finally, cracking at low temperatures and moisture damage leads to a decrease in the serviceability of asphalt pavement in cold climates relative to temperate climates. Hence, a comprehensive and accurate program is necessary to estimate the fracture toughness and moisture susceptibility of asphalt mixtures in cold climates. In recent years, nanotechnology has become very popular due to its unique features in enhancing the operation of bitumen and asphalt mixtures. For this purpose, in this study, the impact of nano-TiO2 on pavement performance against cracking and moisture susceptibility is investigated. To achieve this objective, SCB specimens were fabricated with different ratios of nano-TiO2 (0.0% and 0.9%) and studied at the three temperatures of −5°C, −15°C, and −25°C under pure mode I, pure mode II, and four distinct mixed-mode (I/II) loading (Me=0.2, Me=0.4, Me=0.6, Me=0.8) for various crack geometry, including vertical and angular cracks for which the crack angle is 45° in samples with angular cracks. In addition, the indirect tensile strength (ITS) test was employed to estimate the moisture susceptibility. The results indicated that modifying the asphalt mixture properties with 0.9% nano-TiO2 had a significant impact on the fracture behavior of the samples in both vertical and angular cracks under all temperatures. Additionally, with the application of nano-TiO2 and decreasing temperature, the fracture toughness of the samples increased. Furthermore, the findings displayed that the employment of 0.9% nano-TiO2 reduced the moisture susceptibility of asphalt mixtures by approximately 6%.

Prediction of Crack Propagation of Nano-Crystalline Coating Material Prepared from (SAM2X5): Experimentally and Numerically

The fracture and crack growth of materials can be practically and conveniently predicted through numerical analysis and linear elastics fracture mechanics. On this basis, the current study aims to present experimental work supported by a numerical technique for mimicking the crack propagation by Version 5.6 of COMSOL Multiphysics (version 5.6), used for the simulation of the coating made from Fe-based amorphous material with a thickness of 300 µm. The paper shows the effects of mixed-mode loading on cohesive zone parameters attained from load-crack mouth opening displacement (CMOD) curves. The microstructure dominates the fracture, which in mode I is altered from all-transgranular cleavage to nearly all-intergranular structure in mode II. Two common criteria for failure are linked to the mixed-mode results: Maximum energy release rate criterion (Maximum G) and maximum tensile stress criterion (Maximum S). However, distinguishing between the two criteria is made impossible by the large scatter in the data. The stress intensity factor is the basis for the. The stress intensity factor is the leading parameter facilitated by the singular element and should be estimated with accuracy. With the aim of comparing each criterion and illustrating the numerical schemes’ robustness, a number of examples are presented. It can be concluded that the Maximum G and Maximum S were successful and accurate in predicting the propagation of the Fe-based amorphous material prepared on mild steel.

Investigating the effect of raster orientation on fracture behavior of 3D-printed ABS specimens under tension-tear loading

Most of the engineering components are servicing under complex loading conditions or have complex geometries that lead to a multiaxial stress state in the component. Thus, the fracture behavior of parts under mixed-mode loading conditions should be investigated. The Fused Deposition Modeling (FDM) is a subcategory of the Additive Manufacturing (AM) techniques that has some important manufacturing parameters. The raster orientation (or raster angle) is one of fabricating parameters that significantly affect the mechanical behavior of fabricated parts. Therefore, this study aims to investigate the fracture behavior of FDM specimens made of Acrylonitrile Butadiene Styrene (ABS) under mixed-mode I/III loading conditions. To this goal, four different raster configurations of ψR = 0/90°, 15/-75°, 30/-60°, and 45/-45° were selected for FDM fabrication of edge cracked rectangular specimens, and five loading angles of β = 0° (mode I), 40°, 65°, 72°, and 90° (mode III) were used for performing mixed-mode I/III fracture experiments on the pre-cracked specimens. Besides, some tensile experiments were performed on dog-bone specimens fabricated with the mentioned raster configurations. In order to theoretically predict the failure loads in the tested cracked specimens, a theoretical model named Equivalent Material Concept (EMC) was utilized for equating the ductile behavior of FDM-ABS material with a brittle one. The mentioned concept was coupled with J-integral (EMC-J) and Maximum Tangential Stress (EMC-MTS) criteria to predict the failure loads under mixed-mode loading conditions. The results showed that both EMC-J and EMC-MTS criteria could predict the experimental failure loads well. Additionally, Scanning Electron Microscopy (SEM) was performed on the fracture surfaces to analyze the failure mechanisms of the tested specimens. SEM analysis confirmed the presence of three failure features namely air gaps, filament pullouts, and hackle regions that were discussed comprehensively.

On reformulating the theory of critical distances to predict strength of notched plain concrete beams under mode I and mixed mode loading

The theory of critical distances (TCD), due to its appealing characteristics, has been successfully used in the past to predict the strength of brittle as well as ductile materials, weakened by the presence of stress risers, under both static and fatigue loading. In this work, the TCD’s unique features are exploited and the point method is reformulated to predict the strength of notched plain concrete beams of different sizes under mode I and mixed mode quasi-static loading. The fracture process zone, which is responsible for the non-linearity of concrete, is considered through the concept of an effective elastic crack. A power law is proposed to relate the effective crack length to the geometrical properties. The material characteristic length, required for application of TCD, is correlated with the maximum aggregate size. The resulting formulation is found to yield satisfactory prediction of static strength of notched plain concrete beams, wherein the geometric dimensions of the beam, tensile strength and maximum aggregate size of the concrete mix are the only input parameters. The proposed formulation is validated using a probabilistic analysis of various experimental results available in the literature.

In situ optical observation of damage and failure process in adhesively bonded CFRP joints under mixed-mode loading

The effects of mode mixity on microscopic damage and failure process in adhesively bonded carbon fiber reinforced plastic (CFRP) joints were studied by in situ observation. Optical microscopy observation revealed that the damage and failure process were largely affected by the mixed-mode ratio of joints. The whitening of the adhesive resin due to cavitation was observed with an increasing mode I component, whereas the plastic zone length increased with an increasing mode II component. The damage and failure process observed by experiment were correlated with the stress state around the crack tip obtained by finite element analysis. The results indicated that the microscopic failure process well reflects the deformation and failure properties of epoxy resin depending on stress triaxiality.

Study on two-dimensional mixed-mode fatigue crack growth employing ordinary state-based peridynamics

Mixed-mode fatigue crack propagation analysis is studied using ordinary state-based peridynamics. By introducing the concept of “remaining life”, the fatigue crack nucleation and propagation can be simulated in the PD framework. The PD fatigue modelling and the crack path prediction is carefully investigated. For the comparison purpose, the maximum circumferential stress criterion is introduced. The interaction integral and the peridynamic differential operator is employed to evaluate the fracture mechanics parameters. Two pre-cracked structures under mixed-mode loading conditions are provided with the validations from reference solutions.

Exploring the potential of the critical shear crack theory for reinforced and post-tensioned glass beams: Initial analysis and experiments

In the evolution of structural glass beam elements, the requirements for post-fracture load bearing capacity and safe failure behaviour have led to the development of reinforced and post-tensioned beams. Maximum bending capacity in the post-fracture state is normally associated with extensive yielding of the reinforcement, providing a safe failure mechanism through apparent ductility of the composite beam section. This can be achieved as long as the propagation of primary flexural cracks does not compromise the transfer of shear from the load points to the supports. Although shear failure is typically not critical for the ultimate limit state design of ’normal’ unreinforced glass beams, it may govern the load-bearing and deformation capacity in the post-fracture state for reinforced and post-tensioned glass beams. This paper presents exploratory experiments and initial analysis of the shear failure phenomenon in the post-fracture state of reinforced and post-tensioned glass beams. Potential shear transfer mechanisms are identified based on the critical shear crack theory developed for reinforced concrete members and applied in the analysis of shear failures observed in four-point bending tests of post-tensioned glass beams. The behaviour of fractured laminated glass under mixed-mode (tension+shear) loading is explored on a limited set of small-scale double-notched glass specimens, demonstrating the feasibility of the applied test methodology. Preliminary findings of the present study may serve as a basis for further investigations of shear resistance of glass beams. Typical shear failure kinematics and suitable constitutive laws of the applied materials need further investigation in order to provide design recommendations for the prediction of shear resistance of reinforced and post-tensioned glass beams.