An approach to calculate the J‐integral by digital image correlation displacement field measurement

This paper presents a combined experimental‐numerical technique for the calculation of the J‐integral as an area integral in cracked specimens. The proposed technique is based on full‐field measurement using digital image correlation (DIC) and the finite element method. The J‐integral is probably the most generalised and widely used parameter to quantify the fracture behaviour of both elastic and elastoplastic materials. The proposed technique has the advantage that it does not require crack length measurements nor is it limited to elastic fracture mechanics, provided that only small scale yielding is present. Evaluated are three test geometries; compact tension, three‐point bend and the double torsion beam. Possible errors and their magnitude and the limitations of the method are considered.     

Extended digital image correlation with crack shape optimization

The methodology of eXtended finite element method is applied to the measurement of displacements through digital image correlation. An algorithm, initially based on a finite element decomposition of displacement fields, is extended to benefit from discontinuity and singular enrichments over a suited subset of elements. This allows one to measure irregular displacements encountered, say, in cracked solids, as demonstrated both in artificial examples and experimental case studies. Moreover, an optimization strategy for the support of the discontinuity enables one to adjust the crack path configuration to reduce the residual mismatch, and hence to be tailored automatically to a wavy or irregular crack path. Copyright © 2007 John Wiley & Sons, Ltd.     

DIC‐based J‐integral evaluation of laser repaired cracks with micro/nanomaterial addition

Cracks generated by a wire electric discharge machining on compact tension specimens are first repaired by high powered laser beam with different weight fractions of nano‐WC added at the crack tip. Digital image correlation method combined with J‐integral theory is used to measure and calculate J‐integrals of the repaired specimens. Fracture properties of the repaired specimens are compared and studied. The residual stress of specimens after being repaired by laser was also studied to analyze the feasibility of J‐integral to evaluate the fracture properties of the repaired parts. It is found that the influence of residual stress can be neglected when calculating J‐integral in a certain region in case of when the residual stress is small. The J‐integral obtained by the digital image correlation measurement is accurate and can effectively evaluate repairing effects. The paper provides guidance for laser repaired cracks with nanomaterial addition and an effective method for the evaluation of repairing effect.     

Time‐resolved integrated digital image correlation

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd.     

Local strain accumulation in fatigue crack propagation process of Ti‐6Al‐4V alloy

Fatigue crack growth behaviours of the titanium alloy Ti‐6Al‐4V, with two different microstructures, at different maximum stresses were identified by digital image correlation technique. Full‐field strains were monitored around fatigue cracks after consecutive cycles in fatigue crack growth experiments. Results indicated that the Ti‐6Al‐4V alloy with a bi‐modal microstructure had a better fatigue resistance than that with a primary‐α microstructure. Typical behaviours of small cracks and the evolution of multi‐scale fatigue cracks were clarified. The strain accumulations around the micro‐notch and fatigue crack increased with increasing number of load cycles. On the basis of von Mises strain mapping, it was found that crack growth rate could be characterized by crack‐tip plastic zone size.     

Single‐camera special stereo‐digital image correlation applied for accurate virtual fields method identification

A single‐camera special stereo‐DIC (SS‐DIC) is proposed for accurate virtual fields method (VFM) identification. The single‐camera SS‐DIC allows accurate surface 3D deformation measurements using a single colour camera and a specially designed colour separation device. It not only effectively eliminates the unavoidable out‐of‐plane movement/rotation due to unideal in‐plane loading but also delivers uniformly distributed measurement points that brings great simplicity and convenience for internal virtual work calculation in VFM. In addition, since only a single camera is used for stereovision, the proposed SS‐DIC system requires no complicated synchronisation devices. The effectiveness and practicality of the proposed method are evaluated by heterogeneous deformation experiments of a holed aluminium alloy and 304 stainless steel plate. Combined with a high‐speed colour camera, the proposed method is expected to be a simple and practical method for the calibration of material constitutive model under intermediate and high strain rate conditions using VFM.     

Plastic CTOD as fatigue crack growth characterising parameter in 2024‐T3 and 7050‐T6 aluminium alloys using DIC

The plastic range of crack tip opening displacement (CTOD) has been used for the experimental characterisation of fatigue crack growth for 2024‐T3 and 7050‐T6 aluminium alloys using digital image correlation (DIC). Analysis of a complete loading cycle allowed resolving the CTOD into elastic and plastic components. Fatigue tests were conducted on compact tension specimens with a thickness of 1 mm and a width of 20 mm at stress ratios of 0.1, 0.3 and 0.5. The range of plastic CTOD could be related linearly to da/dN independent of stress ratio for both alloys. To facilitate accurate measurements of CTOD, a method was developed for correctly locating the crack tip and a sensitivity analysis was performed to explore the effect of measurement position behind the crack tip on the CTOD. The plastic range of CTOD was demonstrated to be a suitable alternate parameter to the stress intensity factor range for characterising fatigue crack propagation. A particularly innovative aspect of the work is that the paper describes a DIC‐based technique that the authors believe gives a reliable way to determine the appropriate position to measure CTOD.     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

Fatigue damage analysis in a duplex stainless steel by digital image correlation technique

Strain field measurements by digital image correlation today offer new possibilities for analysing the mechanical behaviour of materials in situ during mechanical tests. The originality of the present study is to use this technique on the micro-structural scale, in order to understand and to obtain quantitative values of the fatigue surface damage in a two-phased alloy. In this paper, low-cycle fatigue damage micromechanisms in an austenitic-ferritic stainless steel are studied. Surface damage is observed in real time, with an in situ microscopic device, during a low-cycle fatigue test performed at room temperature. Surface displacement and strain fields are calculated using digital image correlation from images taken during cycling. A detailed analysis of optical images and strain fields measured enables us to follow precisely the evolution of surface strain fields and the damage micromechanisms. Firstly, strain heterogeneities are observed in austenitic grains. Initially, the austenitic phase accommodates the cyclic plastic strain and is then followed by the ferritic phase. Microcrack initiation takes place at the ferrite/ferrite grain boundaries. Microcracks propagate to the neighbouring austenitic grains following the slip markings. Displacement and strain gradients indicate probable microcrack initiation sites.     

Subpixel precision of crack lip movements by Heaviside-based digital image correlation for a mixed-mode fracture

This study reports on the Heaviside-based digital image correlation (H-DIC) procedure and its application in fracture analysis. This improved DIC procedure was proposed to solve the uncertainty problems at the vicinity of the crack and to evaluate the opening and shear movements of crack lips and the orientations of cracks in the subset. Some tests were conducted to demonstrate the performance of the H-DIC algorithm. An application on argillaceous rock mass exhibiting multiple mixed-mode fractures is shown to validate the efficiency and robustness of the proposed method. This application consisted in processing images acquired from an experimental investigation performed in a gallery front submitted to climatic seasonal variations. The results illustrated how the H-DIC procedure enables to localise and to quantify the opening, shearing and orientation of subpixel cracks. A sensibility study performed on the opening and shear components demonstrated that the precision of crack aperture by H-DIC procedure is close to 0.14 pixel and the spatial resolution is equal to one pixel. Moreover, the crack area was calculated from local apertures on a monitoring duration of 1 year, and a maximum value of 595.8 mm² in winter was obtained.     

A single camera three‐dimensional digital image correlation system for the study of adiabatic shear bands

We describe the capability of a high‐resolution three‐dimensional digital image correlation (DIC) system specifically designed for high strain‐rate experiments. Utilising open‐source camera calibration and two‐dimensional DIC tools within the MATLAB framework, a single camera three‐dimensional DIC system with submicron displacement resolution is demonstrated. The system has a displacement accuracy of up to 200 times the optical spatial resolution, matching that achievable with commercial systems. The surface strain calculations are benchmarked against commercially available software before being deployed on quasi‐static tests showcasing the ability to detect both in‐ and out‐of‐plane motion. Finally, a high strain‐rate (1.2×10³ s^?1) test was performed on a top‐hat sample compressed in a split‐Hopkinson pressure bar in order to highlight the inherent camera synchronisation and ability to resolve the adiabatic shear band phenomenon.     

NiCr/ZrO2功能梯度复合材料中混合型准静态裂纹启裂的数字散斑相关方法实验研究

采用粉末冶金方法制备出NiCr/ZrO₂功能梯度材料FGMs。通过2种断裂试件研究了材料梯度对混合型断裂行为的影响(FGM-A试件,裂纹位于试件的弹性模量较大一侧;FGM-B试件,裂纹位于试件的弹性模量较小一侧)。对2种断裂试件在非对称载荷下进行准静态断裂实验,并利用数字散斑相关方法测得Ⅰ、Ⅱ型应力强度因子。结果表明：FGM-A的裂纹的开裂角小于FGM-B的开裂角;FGM-A的弹性梯度对静态裂纹有保护作用;弹性模量的梯度变化和裂尖局部材料的断裂韧性会影响混合型裂纹的启裂。     

A meshless method with enriched weight functions for three‐dimensional crack propagation

The propagation of cracks in three dimensions is analysed by a meshless method. The cracks are modelled by a set of triangles that are added when the propagation occurs. Since the method is meshless, no remeshing of the domain is necessary during the propagation. To avoid using a large number of degrees of freedom, the stress singularity along the front of the cracks is taken into account by an enrichment of the shape functions of the meshless method by means of appropriate weight functions. This enrichment technique is an extension of the technique that proved to be successful in two dimensions in a previous paper. Several algorithms for efficiently implementing the meshless method in three dimensions are detailed. The accuracy of the enrichment is first assessed on simple examples and some results of non‐planar propagation of multiple cracks are then presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Impact of motion blur on stereo‐digital image correlation with the focus on a drone‐carried stereo rig

Stereo‐digital image correlation (DIC) is a wide‐spread technique in the field of experimental mechanics for measuring shape, motion, and deformation and it is frequently used for material identification by using inverse methods (e.g., virtual fields method and finite element model updating). New applications emerge due to the reached maturity level of the technique, which poses new challenges towards reaching a desired level of accuracy in operating conditions. In this work, the possibility of a drone carrying an in‐house‐made portable DIC setup is explored, and the effect of the drone‐induced vibrations on the accuracy of stereo‐DIC for shape and strain measurement is evaluated. During acquisition, the relative motion between the camera system and the measured item generates motion‐blurred images. The effect of this phenomenon on the precision of stereo‐DIC is further evaluated in this paper.     

Fatigue crack growth law of API X80 pipeline steel under various stress ratios based on J‐integral

Load‐controlled three‐point bending fatigue tests were conducted on API X80 pipeline steel to investigate the effects of stress ratio and specimen orientation on the fatigue crack growth behaviour. Because of the high strength and toughness of X80 steel, crack growth rate was measured and plotted versus ΔJ with stress ratio. The fatigue crack length is longer in the transverse direction, whereas the fatigue crack growth rates are nearly the same in different orientations. Finally, a new fatigue crack growth model was proposed. The effective J‐integral range was modified by ΔJ_p in order to correlate crack closure effect due to large‐scale yield of crack tip. The model was proved to fit well for fatigue crack growth rate of API X80 at various stress ratios of R > 0.     

Empirical model for plasticity‐induced crack closure based on Kmax and ΔK

The mean stress has a significant effect on crack propagation life and must be included in prediction models. However, there is no consensus in the fatigue community regarding the dominant mechanism explaining the mean stress effect. The concept of crack closure has been widely used and several empirical models can be found in literature. The stress ratio, R, is usually the main parameter of these models, but present numerical results showed a significant influence of K_max. A new empirical model is therefore proposed here, dependent on K_max and ΔK, with four empirical constants. The model also includes the effect of material's yield stress, and two additional parameters were defined to account for stress state and crack closure parameter. A comparison was made with Kujawski's and Glinka's parameters, for a wide range of loading conditions. ΔK_eff lies between Kujawski's and Glinka's parameters, and some agreement is evident, although the concepts are quite different. The crack opening model was applied to literature results and was able to collapse da/dN–ΔK curves for different stress ratios to a single master curve.     

Modelling on crack propagation behaviours at concrete matrix‐aggregate interface

A numerical model is proposed to simulate crack propagation at concrete matrix‐aggregate interface. One single aggregate surrounded by concrete matrix is taken to demonstrate the behaviours of crack penetration into concrete matrix and crack growth along the interface. Influences of side‐edge constraint, aggregate direction, and interface fracture energy on the crack propagation behaviours are respectively investigated. The results show that, tensile constraint on the side edge, a smaller angle between tensile axis and aggregate, and higher fracture energy lead to a higher rupture strength of the interface. Once the interface crack starts to grow, it propagates to the two ends of aggregate major axis drastically and further penetrates into the matrix. Nevertheless, these factors have no appreciable influence on crack propagation path. By mapping interface crack into major axis, ordinary crack is generated. Using the above simplification, modelling of multiple crack propagation in concrete is efficiently achieved.     

Fatigue crack propagation characteristics of high‐tensile steel wires for bridge cables

The viability of single edge cracked sheet test method for rapidly determining the crack propagation characteristics of steel wires was investigated. First, fatigue tests under 3 different stress ratios were conducted on the sheet specimens which were manufactured from a kind of widely used cable wires. The test data were analysed, and the crack growth rates of sheet specimens were constructed by Walker model. Then, a series of fatigue tests were performed on notched round‐bar specimens to verify the predictability of Walker model parameters. Moreover, the experimental results obtained in different studies on crack propagation characteristics of steel wires were discussed. The results show that the crack propagation characteristics of sheet specimens behave a certain dependence on depth. The sheet crack growth laws can be well used to predict the fatigue life of notched bar specimens when the mechanical heterogeneity is considered. For bridge cable steels, the rational values for the exponent parameter of Paris law, m, should be close to 3.