Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

For many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

Polymer‐Passivated Inorganic Cesium Lead Mixed‐Halide Perovskites for Stable and Efficient Solar Cells with High Open‐Circuit Voltage over 1.3 V

Cesium‐based trihalide perovskites have been demonstrated as promising light absorbers for photovoltaic applications due to their superb composition stability. However, the large energy losses (E_loss) observed in inorganic perovskite solar cells has become a major hindrance impairing the ultimate efficiency. Here, an effective and reproducible method of modifying the interface between a CsPbI₂Br absorber and polythiophene hole‐acceptor to minimize the E_loss is reported. It is demonstrated that polythiophene, deposited on the top of CsPbI₂Br, can significantly reduce electron‐hole recombination within the perovskite, which is due to the electronic passivation of surface defect states. In addition, the interfacial properties are improved by a simple annealing process, leading to significantly reduced energy disorder in polythiophene and enhanced hole‐injection into the hole‐acceptor. Consequently, one of the highest power conversion efficiency (PCE) of 12.02% from a reverse scan in inorganic mixed‐halide perovskite solar cells is obtained. Modifying the perovskite films with annealing polythiophene enables an open‐circuit voltage (V_OC) of up to 1.32 V and E_loss of down to 0.5 eV, which both are the optimal values reported among cesium‐lead mixed‐halide perovskite solar cells to date. This method provides a new route to further improve the efficiency of perovskite solar cells by minimizing the E_loss.     

Stress‐Strength Reliability Analysis with Extreme Values based on q‐Exponential Distribution

When dealing with practical problems of stress–strength reliability, one can work with fatigue life data and make use of the well‐known relation between stress and cycles until failure. For some materials, this kind of data can involve extremely large values. In this context, this paper discusses the problem of estimating the reliability index R = P(Y < X) for stress–strength reliability, where stress Y and strength X are independent q‐exponential random variables. This choice is based on the q‐exponential distribution's capability to model data with extremely large values. We develop the maximum likelihood estimator for the index R and analyze its behavior by means of simulated experiments. Moreover, confidence intervals are developed based on parametric and nonparametric bootstrap. The proposed approach is applied to two case studies involving experimental data: The first one is related to the analysis of high‐cycle fatigue of ductile cast iron, whereas the second one evaluates the specimen size effects on gigacycle fatigue properties of high‐strength steel. The adequacy of the q‐exponential distribution for both case studies and the point and interval estimates based on maximum likelihood estimator of the index R are provided. A comparison between the q‐exponential and both Weibull and exponential distributions shows that the q‐exponential distribution presents better results for fitting both stress and strength experimental data as well as for the estimated R index. Copyright © 2016 John Wiley & Sons, Ltd.     

Calculation of the crack tip parameters in the holed‐cracked flattened Brazilian disk (HCFBD) specimens under wide range of mixed mode I/II loading

In this paper, the crack tip parameters including the stress intensity factors (K_I and K_II), T‐stress and the third terms of the stress field (A₃ and B₃) are determined comprehensively for a disk‐type sample named holed‐cracked flattened Brazilian disk (HCFBD) under various combinations of mode I and mode II loading. The HCFBD specimen is a circular disk containing a central hole in which the initial cracks are created radially from the hole circumference. Moreover, the ends of HCFBD are flattened for the sake of convenient loading. Performing enormous finite element analyses and calculating the stress intensity factors K_I and K_II, the states of pure mode II are determined for different configurations of HCFBD. Furthermore, the sign and magnitude of parameter A₃ which plays an important role to justify the geometry and size effects on the fracture toughness of quasi‐brittle materials are also determined for HCFBD with different geometrical ratios.     

On the notch sensitivity of flax fibre metal laminates under static and fatigue loading

Damage progression and failure characteristics of open‐hole flax fibre aluminium laminate (flax‐FML) specimens subjected to quasi‐static tensile or tension‐tension fatigue loading were experimentally investigated. Notched and unnotched flax‐FML composites exhibited brittle fracture with little or no fibre pull‐out and minimal delamination at the aluminium/adhesive interface. The flax‐FMLs were tested to failure under tension‐tension fatigue loading conditions (R ratio of 0.1; frequency of 10 Hz; applied fatigue stresses ranging between 30% and 80% of the respective ultimate tensile strength values). The fatigue cycles to failure decreased with the increase in the applied fatigue stress and hole diameter. A phenomenological modelling technique was developed to evaluate the fatigue life of an open‐hole flax‐FML composite. Fatigue tests on specimens subjected to a maximum load equivalent to 35% of the respective tensile failure strength were interrupted at around 85% of the corresponding fatigue life. The accumulated fatigue damage in these specimens was characterised using X‐ray computed tomography. For benchmarking purposes, the fatigue performance and related damage progression in the flax‐FML composite were compared with those of the glass‐FMLs.     

All‐Solution‐Processed Pure Formamidinium‐Based Perovskite Light‐Emitting Diodes

All‐solution‐processed pure formamidinium‐based perovskite light‐emitting diodes (PeLEDs) with record performance are successfully realized. It is found that the FAPbBr₃ device is hole dominant. To achieve charge carrier balance, on the anode side, PEDOT:PSS 8000 is employed as the hole injection layer, replacing PEDOT:PSS 4083 to suppress the hole current. On the cathode side, the solution‐processed ZnO nanoparticle (NP) is used as the electron injection layer in regular PeLEDs to improve the electron current. With the smallest ZnO NPs (2.9 nm) as electron injection layer (EIL), the solution‐processed PeLED exhibits a highest forward viewing power efficiency of 22.3 lm W^?1, a peak current efficiency of 21.3 cd A^?1, and an external quantum efficiency of 4.66%. The maximum brightness reaches a record 1.09 × 10⁵ cd m^?2. A record lifetime T₅₀ of 436 s is achieved at the initial brightness of 10 000 cd m^?2. Not only do PEDOT:PSS 8000 HIL and ZnO NPs EIL modulate the injected charge carriers to reach charge balance, but also they prevent the exciton quenching at the interface between the charge injection layer and the light emission layer. The subbandgap turn‐on voltage is attributed to Auger‐assisted energy up‐conversion process.     

Highly Efficient p‐i‐n Perovskite Solar Cells Utilizing Novel Low‐Temperature Solution‐Processed Hole Transport Materials with Linear π‐Conjugated Structure

Alternative low‐temperature solution‐processed hole‐transporting materials (HTMs) without dopant are critical for highly efficient perovskite solar cells (PSCs). Here, two novel small molecule HTMs with linear π‐conjugated structure, 4,4′‐bis(4‐(di‐p‐toyl)aminostyryl)biphenyl (TPASBP) and 1,4′‐bis(4‐(di‐p‐toyl)aminostyryl)benzene (TPASB), are applied as hole‐transporting layer (HTL) by low‐temperature (sub‐100 °C) solution‐processed method in p‐i‐n PSCs. Compared with standard poly(3,4‐ethylenedioxythiophene): poly(styrenesulfonic acid) (PEDOT:PSS) HTL, both TPASBP and TPASB HTLs can promote the growth of perovskite (CH₃NH₃PbI₃) film consisting of large grains and less grain boundaries. Furthermore, the hole extraction at HTL/CH₃NH₃PbI₃ interface and the hole transport in HTL are also more efficient under the conditions of using TPASBP or TPASB as HTL. Hence, the photovoltaic performance of the PSCs is dramatically enhanced, leading to the high efficiencies of 17.4% and 17.6% for the PSCs using TPASBP and TPASB as HTL, respectively, which are ≈40% higher than that of the standard PSC using PEDOT:PSS HTL.     

A continuum damage mechanics method for fracture simulation of quasi‐brittle materials

This paper addresses a novel continuum damage‐based method for simulating failure process of quasi‐brittle materials starting from local damage initiation to final fracture. In the developed method, the preset characteristic length field is used to evaluate damage instead of element, which is used to reduce the spurious sensitivity. In addition, damage is only updated in the most dangerous location at a time for considering stress redistribution due to damage evolution, which is used to simulate competitive fracture process. As cases study, representative numerical simulations of two benchmark tests are given to verify the performance of the developed continuum damage‐based method together with a used damage model. The simulation results of the crack paths for two concrete specimens obtained from the developed method matched well with the corresponding experimental results. The results show that the developed continuum damage‐based method is effective and can be used to simulate damage and fracture process of brittle or quasi‐brittle materials. And the simulation results based on the developed method depend only the preset characteristic length field and not grid mesh.     

Zero Linear Compressibility in Nondense Borates with a “Lu‐Ban Stool”‐Like Structure

Discovering materials that exhibit zero linear compressibility (ZLC) behavior under hydrostatic pressure is extremely difficult. To date, only a handful of ZLC materials have been found, and almost all of them are ultrahard materials with densified structures. Here, to explore ZLC in nondense materials, a structural model analogous to the structure of the “Lu‐Ban stool,” a product of traditional Chinese woodworking invented 2500 years ago, is proposed. The application of this model to borates leads to the discovery of ZLC in AEB₂O₄ (AE = Ca and Sr) with the unique “Lu‐Ban stool”‐like structure, which can obtain a subtle mechanical balance between pressure‐induced expansion and contraction effects. Coupled with the very wide ultraviolet transparent windows, the ZLC behavior of AEB₂O₄ may result in some unique but important applications. The applications of the “Lu‐Ban stool” model open a new route for pursuing ZLC materials in nondense structural systems.     

Graded Heterojunction Engineering for Hole‐Conductor‐Free Perovskite Solar Cells with High Hole Extraction Efficiency and Conductivity

Despite great progress in the photovoltaic conversion efficiency (PCE) of inorganic–organic hybrid perovskite solar cells (PSCs), the large‐scale application of PSCs still faces serious challenges due to the poor‐stability and high‐cost of the spiro‐OMeTAD hole transport layer (HTL). It is of great fundamental importance to rationally address the issues of hole extraction and transfer arising from HTL‐free PSCs. Herein, a brand‐new PSC architecture is designed by introducing multigraded‐heterojunction (GHJ) inorganic perovskite CsPbBr_x I_3?x layers as an efficient HTL. The grade adjustment can be achieved by precisely tuning the halide proportion and distribution in the CsPbBr_x I_3?x film to reach an optimal energy alignment of the valance and conduction band between MAPbI₃ and CsPbBr_x I_3?x . The CsPbBr_x I_3?x GHJ as an efficient HTL can induce an electric field where a valance/conduction band edge is leveraged to bend at the heterojunction interface, boosting the interfacial electron–hole splitting and photoelectron extraction. The GHJ architecture enhances the hole extraction and conduction efficiency from the MAPbI₃ to the counter electrode, decreases the recombination loss during the hole transfer, and benefits in increasing the open‐circuit voltage. The optimized HTL‐free PCS based on the GHJ architecture demonstrates an outstanding thermal stability and a significantly improved PCE of 11.33%, nearly 40% increase compared with 8.16% for pure HTL‐free devices.     

Combined continuum damage‐embedded discontinuity model for explicit dynamic fracture analyses of quasi‐brittle materials

In this paper, a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi‐brittle failure phenomena. The model is capable of describing the rate‐dependent behavior in dynamics and the three phases in failure of quasi‐brittle materials. The first phase is always linear elastic, followed by the second phase corresponding to fracture‐process zone creation, represented with rate‐dependent continuum damage with isotropic hardening formulated by utilizing consistency approach. The third and final phase, involving nonlinear softening, is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions. The proposed model is capable of describing the rate‐dependent ductile to brittle transition typical of cohesive materials (e.g., rocks and ice). The model is implemented in the finite element setting by using the CST elements. The displacement jump vector is solved for implicitly at the local (finite element) level along with a viscoplastic return mapping algorithm, whereas the global equations of motion are solved with explicit time‐stepping scheme. The model performance is illustrated by several numerical simulations, including both material point and structural tests. The final validation example concerns the dynamic Brazilian disc test on rock material under plane stress assumption. Copyright © 2014 John Wiley & Sons, Ltd.     

Shock-wave compression of brittle solids

Extensive experimental investigation in the form of large-amplitude, nonlinear wave-profile measurements which manifest the shock strength and equation-of-state properties of brittle solids has been performed. Brittle materials for which a base of dynamic property data is available include Al₂O₃, AlN, B₄C, CaCO₃, SiC, Si₃N₄, SiO₂ (quartz and glass), TiB₂, WC and ZrO₂. Planar impact methods and velocity interferometry diagnostics have been used exclusively to provide the high-resolution shock-profile data. These wave-profile data are providing engineering dynamic strength and equation-of-state properties as well as controlled, shock-induced motion histories for the validation of theoretical and computational models. Of equal importance, such data are providing a window into the physics of a newly emerging understanding of the compression and deformation behavior of high-strength brittle solids. When considered along with a rich assortment of strength and deformation data in the literature, a systematic assessment of this shock-wave data lends strong support for failure waves and concomitant high-confinement dilatancy as a general mechanism of inelastic deformation in the shock compression of ceramics. Phase transformation in selected brittle solids appears to be a critical state phenomenon strongly controlled by kinetics. The risetime and structure of deformation shock waves in brittle solids are controlled by viscous effects which at present are still poorly understood. The shock-wave data also suggest that both crystalline plasticity and brittle fracture may play important and interconnected roles in the dynamic failure process.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

Interference fit effect on improving fatigue life of a holed single plate

This paper deals with the influence of interference fit coupling on the fatigue strength of holed plates made of a medium‐carbon forging steel (35 KB2), heat treated by quenching followed by tempering, up to a hardness of about 350 BH, obtaining a sorbitic microstructure. Tensile and impact tests showed an ultimate tensile strength of about 1100 MPa, a yield strength of about 1000 MPa, an elongation to failure of 15% and an impact toughness KV of 43 J at room temperature. Axial fatigue tests were performed on holed specimens with or without a pin, made of the same material, press fitted and still left into their central hole. The tension–tension fatigue tests have been performed with a stress ratio R = 0.1. The effect on fatigue strength was investigated both experimentally and numerically. Three different conditions were investigated by using open hole specimens, specimens with 0.6% of nominal specific interference and specimens with 2% of nominal specific interference. The experimental stress‐life (S–N) curves pointed out an increased fatigue life of the interference fit specimens, compared with the open hole ones. The numerical investigation was performed in order to analyse the stress field by applying an elastic plastic 2D simulation, with commercial finite element software. The stress history and distribution around the interference‐fitted hole indicate a significant reduction of the stress amplitude produced by the external loading (remote stress) because a residual and compressive stress field is generated by the pin insertion.     

A cumulative damage model for fatigue life estimation of high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes

A cumulative fatigue damage model is presented to estimate fatigue life for high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes with fish‐eye mode failure, and a simple formula is obtained. The model takes into account the inclusion size, fine granular area (FGA) size, and tensile strength of materials. Then, the ‘equivalent crack growth rate’ of FGA is proposed. The model is used to estimate the fatigue life and equivalent crack growth rate for a bearing steel (GCr15) of present investigation and four high‐strength steels in the literature. The equivalent crack growth rate of FGA is calculated to be of the order of magnitude of 10^?14–10^?11 m/cycle. The estimated results accord well with the present experimental results and prior predictions and experimental results in the literature. Moreover, the effect of inclusion size on fatigue life is discussed. It is indicated that the inclusion size has an important influence on the fatigue life, and the effect is related to the relative size of inclusion for FGA. For the inclusion size close to the FGA size, the former has a substantial effect on the fatigue life. While for the relatively large value of FGA size to inclusion size, it has little effect on the fatigue life.     

Low‐cycle fatigue of IN 718: Effect of waveform

The influence of various strain waveforms on the low‐cycle fatigue of IN 718 tested at 650°C has been investigated. The straining paths are accompanied by dwell‐induced creep component(s) or unequal strain distribution in different portions of cycles reducing strength of material. The investigation intends to clarify mainly mechanistic aspects of relaxation‐fatigue interaction. Features of time‐dependent effect induced by nonpeak dwell and the same accompanied by peak dwell, slow unloading from the peak to a lower strain, and different loading and unloading rates are compared in terms of stress amplitude responses, mean stress relaxation, hysteresis loops, life, and damage parameter D_C‐F. Softening is common in all the cases, and degree of softening varies linearly with life. The energy‐based life prediction model has been found to work well for the data, and we have introduced energy fraction–based approach to observe simultaneous contribution from both creep and fatigue on life.     

Analysis of automotive mixed‐adhesive joints weakened by moist conditions: Experimental characterization and numerical simulation using cohesive zone model

This paper is mostly concerned with an experimental and numerical study to clarify the behaviour and failure in the mono‐adhesive joints and mixed‐adhesive joints under different environmental conditions (dry [E₀], 75.3% relative humidity [E₁], 84.2% relative humidity [E₂], and submerged in tap water [E₃] at 25°C) and different strain rates (1 and 100 mm/min). Experimental investigations are compared with the numerical analysis, which is carried out by bilinear cohesive zone model (CZM). Through this work, degradations of cohesive parameters are calculated by using open‐faced double cantilever beam (DCB) and end notch flexure (ENF) specimens. The experimental data show that the cohesive parameters of Araldite 2015 have negative correlation to moisture content. Although Araldite AV138 parameters experience a decrease in mode I, in mode II, its cohesive parameter increases. First, it is found that the decrease in experimental failure load of mixed‐adhesive joints with regard to the dry condition is recorded as 32.6%, 54%, and 59.1% for E₁, E₂, and E₃ conditions, respectively. Following this further, single lap joint (SLJ) that has non‐uniform moisture content distribution is modelled by engaging specific CZM parameters related to the specific moisture content. The results show a good agreement between experimental and numerical data.     

Modelling the dependency of the Smith–Watson–Topper parameter on the cycles‐to‐failure using serial hybrid neural networks

Calculating the fatigue damage with a strain‐based approach requires an ?–N durability curve that links the strain amplitude to the corresponding number of cycles‐to‐failure. This ?–N curve is usually modelled by the Coffin–Manson relationship. If a loading mean‐level also needs to be considered, the original Coffin–Manson relationship is modified using a Smith–Watson–Topper parameter. In this article a methodology for modelling the dependence of the Smith–Watson–Topper parameter on the number of cycles‐to‐failure is presented. The core of the presented methodology represents a multilayer perceptron neural network combined with the Smith–Watson–Topper analytical model. The article presents the theoretical background of the methodology, which is applied for the case of the experimental fatigue data. The results show that it is possible to model ?–N curves for different influential parameters, such as the specimen's diameter and the testing temperature. The results further show that it is possible to predict ?–N curves even for those combinations of the influential parameters for which no experimental data about the material endurance is available. This fact makes the presented model very suitable for the application in an R&D process when a durability of a product should be estimated on the basis of a very limited set of experimental data about the material endurance characteristics.