Sharp V‐notches in viscoplastic solids: Strain energy rate density rule and fracture toughness

Different from Neuber's rule or Glinka's energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper, the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G‐NSIF) for sharp V‐notch in viscoplastic solids, the concept of SERD for sharp V‐notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SERD, the averaged strain energy density (SED) for sharp V‐notch in viscoplastic solids is derived with integration of time. The fracture toughness relation between sharp V‐notch specimens and crack specimen in viscoplastic materials is given based on the transformation of SERD. A numerical approach is presented to compute the SERD and SED based on finite element method. Some crucial comments on the G‐NSIF have been discussed. Some typical solutions for SERD and SED for sharp V‐notched specimens are investigated.     

Numerical and experimental investigation of mixed‐mode fracture parameters on silicon nitride using the Brazilian disc test

Engineering applications of ceramics can often involve mixed‐mode conditions involving both tensile and shear loading. Mixed‐mode fracture toughness parameters are evaluated for applicability to ceramics using the Brazilian disc test on silicon nitride. Semi‐elliptical centrally located surface flaws are induced on the disc specimens using Vickers indentation and compression loaded to fracture with varying levels of mode mixity. The disc specimens are modelled via 3D finite element analysis and all three modes of stress intensity factors computed along the crack front, at failure load. We present a numerical and experimental investigation of four widely used mixed‐mode fracture criteria and conclude that the critical strain energy release rate criterion is simple to implement and effective for silicon nitride under mixed‐mode conditions.     

A New Procedure for Mode I Fracture Characterization of Cement‐Based Materials

Fracture characterization under mode I loading of a cement‐based material using the single‐edge‐notched beam loaded in tree‐point‐bending was performed. A new method based on beam theory and crack equivalent concept is proposed to evaluate the Resistance‐curve, which is essential to determine fracture toughness with accuracy. The method considers the existence of a stress relief region in the vicinity of the crack, dispensing crack length monitoring during experiments. A numerical validation was performed by finite element analysis considering a bilinear cohesive damage model. Experimental tests were performed in order to validate the numerical procedure. Digital image correlation technique was used to measure the specimen displacement with accuracy and without interference. Excellent agreement between numerical and experimental load–displacement curves was obtained, which validates the procedure.     

A computational strategy for damage‐tolerant design of hollow shafts under mixed‐mode loading condition

Three‐dimensional numerical analyses, using the finite element method (FEM), have been adopted to simulate fatigue crack propagation in a hollow cylindrical specimen, under pure axial or combined axial‐torsion loading conditions. Specimens, made of Al alloys B95AT and D16T, have been experimentally tested under pure axial load and combined in‐phase constant amplitude axial and torsional loadings. The stress intensity factors (SIFs) have been calculated, according to the J‐integral approach, along the front of a part through crack, initiated in correspondence of the outer surface of a hollow cylindrical specimen. The crack path is evaluated by using the maximum energy release rate (MERR) criterion, whereas the Paris law is used to calculate crack growth rates. A numerical and experimental comparison of the results is presented, showing a good agreement in terms of crack growth rates and paths.     

A new fixture for fracture tests under mixed mode I/II/III loading

In this paper, a new loading device for general mixed mode I/II/III fracture tests is designed and recommended. Finite element analyses are conducted on the proposed apparatus to evaluate the fracture parameters of the tested samples under various mixed mode loading conditions. The numerical results revealed that the designed loading fixture can generate wide varieties of mode mixities from pure tensile mode to pure in‐plane and out‐of‐plane shear modes. The accuracy of the proposed fixture is evaluated by conducting a wide range of fracture tests on compact tension shear (CTS) specimens made of polymethyl methacrylate (PMMA). The experimental results are then compared with the theoretical predictions obtained by the Richard criterion. A good consistency is observed between the experimental results and theoretical predictions.     

A hybrid approach to determine fracture resistance for mode I and mixed‐mode I and II fracture specimens

This paper proposes a hybrid approach to determine the fracture resistance for mode I and mixed‐mode I and II fracture specimens, combining both numerically computed and experimentally measured load (P) versus load‐line displacement (LLD or Δ) relationships for metallic fracture specimens. The hybrid approach predicates on the same principle as the conventional, multiple‐specimen experimental method in determining the energy release rate. The hybrid method computes the P–Δ curves from multiple finite element (FE) models, each with a different crack depth. The experimental procedure measures the P–Δ curve from a standard fracture specimen with a growing crack. The intersections between the experimental P–Δ curve and the numerical P–Δ curves from multiple FE models dictate the LLD levels to compute the strain energy (U) using the area under the numerical P–Δ curves. This method provides accurate estimates of the J resistance data for both SE(B) specimen under mode I loading and single‐edge notched specimens under mixed‐mode I and II loading.     

The effect of volume fraction of primary α phase on fracture toughness behaviour of Timetal 834 titanium alloy under mode I and mixed mode I/III loading

The effect of volume fraction of primary α phase on mode I and mixed mode I/III fracture toughness of Timetal 834 titanium alloy was investigated. The mode I and mixed mode I/III fracture toughness values for loading angle of 30° were found to initially decrease and subsequently increase with increase in volume fraction of primary α phase. On the other hand, mixed mode I/III fracture toughness for loading angle of 45° was found to monotonically decrease with increasing volume fraction of α phase. The fracture toughness was also found to marginally increase with increasing loading angle for the two lower primary α volume fractions, i.e. 6% and 15% whereas it marginally decreases with increasing loading angle for primary α volume fraction of 30%. The results were explained on the basis of the nature of stress field ahead of the crack tip under mixed mode I/III loading as well as the fracture mechanisms operative in this alloy for different α volume fractions.     

A new three‐point approximation approach for design optimization problems

In this paper, a newly developed three‐point approximation scheme is proposed. The expression of this scheme consists of a linear combination of the direct and reciprocal linear Taylor expansions as well as of the lumped diagonal terms of the second‐order direct and inverse terms. The unknown parameters of the expression are computed on the basis of the function and gradient values at three points in the design space. Based on this approach, the accuracy of the existing constraint approximation methods can be improved. The effectiveness of the proposed approach is demonstrated on a number of numerical examples. The numerical results are also compared with those of the previously published work. Copyright © 2001 John Wiley & Sons, Ltd.     

A node release approach to estimate J‐R curve for single‐edge‐notched tension specimen under reversed loading

This paper proposes a node release approach to estimate the fracture resistance curve, often known as the J‐R curve, for monotonic and cyclic fracture tests. The node release approach simulates the crack extension by releasing the constraints imposed on the node at the crack tip and estimates the J‐R curve by coupling the domain integral value with the corresponding crack extension. This proposed node release approach estimates closely the J‐R curve for SE(B) and SE(T) specimens subjected to monotonic loading. For SE(T) specimen under cyclic loading, this study implements the node release analysis in two approaches: (1) an equivalent monotonic analysis corresponding to the envelope of the cyclic load‐CMOD response and (2) a direct cyclic simulation. Both approaches lead to close estimations of the experimentally measured J‐R curve. The numerical analysis also confirms the path independence of the domain integral values in the direct cyclic simulation.     

A new weight function for one‐dimensional subsurface cracks under general loading

In the present study, weight functions (WFs) of a subsurface crack were derived by proposing a new general form for approximate one‐dimensional WF. The WFs coefficients were considered as a function of crack length to depth ratio and were obtained using reference stress intensity factors (SIFs) of 16 cracks under uniform, linear, and parabolic normal and shearing loadings. The verification was performed by comparison of the straight and coupled SIFs calculated by WF and finite element modelling under some complicated loadings. In conclusion, the WFs can be simply and effectively employed for evaluating the cracks under any complex stress distributions.     

A coupled approach of optimization,uncertainty analysis and configurational mechanics for a fail‐safe design of structures

In this contribution, a novel method for a fail‐safe optimal design of structures is proposed, which is a coupled approach of optimization employing a genetic algorithm, the structural analysis conducted in the framework of fracture mechanics and uncertainty analysis. The idea of fail‐safe structures is to keep their functionality and integrity even under damage conditions, for example, a local failure of substructures. In the present work, a design concept of a substructure exhibiting a damage accumulating function due to the application of crack arresters is introduced. If such a substructure is integrated within a system of coupled substructures, it will accumulate the damage arising from the boundary conditions change induced by the failure of certain neighbouring structural elements and hinder further damage escalation. The investigation of failure of the damage accumulating substructure is introduced within a finite element framework by a combination of discrete fracturing and configurational mechanics based criteria. In order to design a structure, which will fail safely according to a predefined scenario, uncertainties are taken into account. The developed approach optimizes the configuration of crack arresters within the damage accumulating substructure so that the uncertain crack propagation is hindered and only a local failure of this element occurs. Copyright © 2016 John Wiley & Sons, Ltd.     

Towards Material Testing 2.0. A review of test design for identification of constitutive parameters from full‐field measurements

Full‐field optical measurements like digital image correlation or the grid method have brought a paradigm shift in the experimental mechanics community. While inverse identification techniques like finite element model updating or the virtual fields method have been the object of significant developments, current test methods, inherited from the age of strain gauges or linear variable displacement transducers, are generally not well adapted to the rich information provided by these new measurement tools. This paper provides a review of the research dealing with the design and optimization of heterogeneous mechanical tests for the identification of material parameters from full‐field measurements, christened here Material Testing 2.0 (MT2.0).     

A new method for modelling the support effect under rotating bending fatigue: application to Ti‐6Al‐4V alloy,with and without shot peening

The subject of this paper is to investigate the capability of the relative stress gradient to properly represent the beneficial effect of residual stress states on the fatigue life of Ti‐6Al‐4V specimens, with notches of different severity. The research was developed considering notched and un‐notched specimens with different geometries and different shot‐peening treatments. The results were determined by running fatigue experimentation under rotating bending and by developing a novel predictive model based on the relationship between the local fatigue limit and a generalized form of the relative stress gradient, accounting for the peening‐induced residual stresses. The proposed tool for fatigue limit estimation was completed by a stochastic analysis, which considered the variability of the involved parameters, in particular the residual stress entity. This made it possible to finally determine the component failure probability in a general, efficient and accurate way.     

A sequential weighted Laplacian‐regularized optimal design for response surface modeling of expensive functions with outliers: An application in linear elastic fracture mechanics

There are several sequential and adaptive strategies designed to reduce the number of experiments in response surface methodology (RSM). However, most of the existing sequential and adaptive methods are sensitive to the existence of possible outliers. In this paper, we propose an active learning methodology based on the fundamental idea of adding a Laplacian penalty to the D‐optimal design and integrate that with robust regression to look for the most informative settings to be measured, while reducing the influence of possible outliers. To leverage the intrinsic geometry of the factor settings in highly nonlinear spaces, we extend the proposed methodology to reproducing Kernel Hilbert space (RKHS). Through an extensive simulation study accompanied by a thorough sensitivity analysis, we show that the proposed framework outperforms traditional RSM designs in the presence of outliers. We also conduct a study utilizing a hierarchical function used in linear elastic fracture mechanics to illustrate practicality of the proposed methodology.