Experimental Investigations of Fracture Process Using DIC in Plain and Reinforced Concrete Beams under Bending

The fracture behaviour of concrete and reinforced concrete beams under quasi‐static three‐point bending was comprehensively investigated with experiments at laboratory scale. The eight various concrete mixes were tested. The influence of the shape, volume and size of aggregate particles and reinforcement on concrete fracture under bending was studied. Displacements on the surface of concrete beams were measured by means of the digital image correlation (DIC) technique. Attention was paid to the formation of a localized zone and its characteristics. In order to avoid the effect of the search patch size and the cut‐off value at displacement and strain profiles, a consistent method was proposed to determine uniformly and accurately the width of a localized zone. Measured surface displacements from DIC were fitted by the error function ERF, whereas surface strains calculated from displacements were fitted by the usual normal distribution (Gauss) function. The width of a localized zone preceding a macro‐crack grew strongly with increasing maximum aggregate size and slightly with diminishing aggregate volume. It did not depend on the aggregate roughness and reinforcement presence.     

Experimental and Numerical Investigation on the Size of Damage Process Zone of a Concrete Specimen under Mixed-Mode Loading Conditions

The characteristic length of a gradient-dependent damage model is a key parameter, which is usually regarded as the length of damage process zone (DPZ). Value and evolution of the size of DPZ were investigated by both a numerical method and an experimental manner. In the numerical study, the geometrical model adopted was a set of four-point shearing beams; the numerical tool used was the Abaqus/Explicit software. The distance between the front and end of a complete DPZ was obtained. Values of strain components at these points were given out at given time points. The experimental study of the evolution process of a damage process zone was investigated with a set of concrete specimens under mixed-mode loading conditions by using a white-light speckle method. The geometrical parameters of the damage process zone were measured. Double-notched specimens under four-point shear loading conditions were adopted. A series of displacement fields for points on the surface of the specimen were measured and further transferred into a strain field of these points during loading process. With reference to the strain values that occurred at both the front and end of a numerically-obtained DPZ, the length of the DPZ was determined with the experimental results. These results provide an experimental basis for the determination of the value of an internal length parameter for a gradient-enhanced and/or area-averaged non-local model.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

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.     

Determination of Ductile Fracture Parameters of a Dual‐Phase Steel by Optical Measurements

Marciniak–Kuczynski and Nakajima tests of the dual‐phase steel Docol 600DL ( www.ssab.com/ ) have been carried out for a range of stress‐states spanning from uniaxial tension to equi‐biaxial tension. The deformation histories of the specimens have been recorded by digital images, and the displacement and strain fields have been determined by post‐processing the images with digital image correlation software. The fracture characteristics of the material are presented by means of the stress triaxiality, the Lode parameter and the equivalent strain. These parameters are evaluated on the surface of the specimens based on the optical field measurements and assumptions regarding the mechanical behaviour of the material. Additionally the minor versus major principal strains up to fracture are presented. It is found that the material displays a significantly lower ductility in plane‐strain tension than in uniaxial tension and equi‐biaxial tension, and that it, in the tests exposed to local necking, undergoes large strains between the onset of necking and fracture. Fractographs of selected specimens reveal that fracture is due to growth and coalescence of voids that occur in localised areas governed by shear‐band instability.     

ANN Model to Predict Fracture Characteristics of High Strength and Ultra High Strength Concrete Beams

This paper presents fracture mechanics based Artificial Neural Network (ANN) model to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (Gf), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). Failure load of the beam (Pmax) is also predicated by using ANN model. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described. Methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. Back-propagation training technique has been employed for updating the weights of each layer based on the error in the network output. Levenberg- Marquardt algorithm has been used for feed-forward back-propagation. Four ANN models have been developed by using MATLAB software for training and prediction of fracture parameters and failure load. ANN has been trained with about 70% of the total 87 data sets and tested with about 30% of the total data sets. It is observed from the studies that the predicted values of Pmax, Gf, failure load, KIc and CTODc are in good agreement with those of the experimental values.     

3D Residual Stress Field in Arteries: Novel Inverse Method Based on Optical Full‐field Measurements

Abstract: Arterial tissue consists of multiple structurally important constituents that have individual material properties and associated stress‐free configurations that evolve over time. This gives rise to residual stresses contributing to the homoeostatic state of stress in vivo as well as adaptations to perturbed loads, disease or injury. The existence of residual stresses in an intact but load‐free excised arterial segment suggests compressive and tensile stresses, respectively, in the inner and outer walls. Accordingly, an artery ring springs open into a sector after a radial cut. The measurement of the opening angle is commonly used to deduce the residual stresses, which are the stresses required to close back the ring. The opening angle method provides an average estimate of circumferential residual stresses but it gives no information on local distributions through the thickness and along the axial direction. To address this lack, a new method is proposed in this article to derive maps of residual stresses using an approach based on the contour method. A piece of freshly excised tissue is carefully cut into the specimen, and the local distribution of residual strains and stresses is determined from whole‐body digital image correlation measurements using an inverse approach based on a finite element model.     

Investigation of the Uncertainty of DIC Under Heterogeneous Strain States with Numerical Tests

Abstract: In this research, numerical 2D digital image correlation (DIC) tests are carried out to assess the uncertainty of DIC under heterogeneous strain states. DIC is implemented to measure the deformation of the numerically deformed images with respect to the undeformed counterparts, which are taken from the real tensile specimens. The tensile specimens are made of three materials, that is, steel DC06, steel DX54D+Z and aluminium alloy Al6016 and cut into three different geometries, namely one standard design and two complex designs. The specimens are all painted manually with random speckle patterns. The original images are deformed by imposed displacement fields, which are obtained by simulating uni‐axial tensile tests of the specimens with finite element analysis (FEA). In this way, the errors sourcing from the hardware of the image system are excluded. According to the geometries of the specimens, homogeneous and heterogeneous strain states are achieved by FEA. The optimum mesh sizes of the models are identified to minimise theirs influence on the imposed fields. The impacts of subset sizes, step sizes and strain window sizes are studied for an optimum correlation. Finally, the influence of the strain state is investigated. It is found that the DIC accuracy and precision decrease under highly heterogeneous strain states.     

An experimental investigation on the FPZ properties in concrete using digital image correlation technique

This paper presents an experimental investigation on the properties of the fracture process zone (FPZ) in concrete using the digital image correlation (DIC) technique. Based on the experimental results, it is found that the FPZ length increases during crack propagation but decreases after the FPZ is fully developed. The FPZ length at the peak load and the maximum FPZ length increase with an increase in specimen height, but decrease by increasing the notch depth to specimen height ratio. It is also found that the crack extension length at the peak load is about 0.25 times the ligament length.     

In situ observation of crack nuclei in poly-granular graphite under ring-on-ring equi-biaxial and flexural loading

Fracture tests of graphite are known to exhibit sensitivity to stress state, such as a difference between their flexural and tensile strengths. Bi-axial tensile and flexural loading are representative of the stress states in some regions of graphite components in nuclear fission reactors, where loading develops from fast neutron irradiation-induced dimensional change and thermal strains. Study of the behaviour of the inherent defects that determine strength variability requires in situ observation of crack nucleation. To this end, digital image correlation can be used to monitor the evolution of displacement fields and hence the cracks on the surface of large samples whilst under load. In this study, a ring-on-ring flexural test setup was developed to apply equi-biaxial tensile stress to large disc specimens of graphite along with the conventional four-point-bend test. A 17% reduction in mean flexural strength was observed for the equi-biaxial loading, relative to uniaxial loading. DIC was used to characterise the observed fracture nuclei. Linear elastic fracture mechanics analysis was shown to be inadequate to explain the strength reduction. It is suggested that fictitious crack models, originally developed to simulate the behaviour of concrete structures, can be utilised to explain the behaviour.     

用有限元分析和DICM确定纸浆模塑材料弹性常数的逆问题

用有限元法分析纸浆模塑包装结构,需要事先确定纸浆模塑材料的弹性常数.基于纸浆模塑薄壁圆锥筒的压缩试验,讨论了可以利用有限元分析和数字相关测量方法(DICM)来识别纸浆模塑材料弹性常数的逆问题.     

On the characteristic distance and minimum fracture toughness for cleavage fracture in a C-Mn steel

This study makes a further investigation on the characteristic distance, minimum fracture toughness and its temperature dependence for cleavage fracture in a C-Mn steel by the detailed finite element analysis combined with experimental observation and measurement. Results show that there is a minimum active zone for cleavage initiation, and the minimum fracture toughness of steel results from the minimum active zone necessary. Corresponding to the minimum fracture toughness, the cleavage fracture ahead of a crack tip can only initiate in a distance range from the minimum distance X_fmin determined by the lower boundary of the active zone to the maximum distance X_fmax determined by its upper boundary. The reason for the occurrence of the minimum active zone and the factors influencing it are analyzed. The temperature dependence of the characteristic distance and minimum fracture toughness and its mechanism are also discussed.     

Crack Extension Resistance and Fracture Properties of Quasi-Brittle Softening Materials like Concrete Based on the Complete Process of Fracture

The crack extension resistance and fracture properties are studied in detail for quasi-brittle materials like concrete with a softening traction-separation law by investigating the complete fracture process. The computed samples are the three-point bending notched beams of concrete with different sizes tested by other researchers. The softening traction-separation law which was proposed by Reinhardt et al. based on direct tension tests for normal concrete materials was chosen in the computations. Different distribution shapes of the cohesive force on the fictitious crack zone were considered for the corresponding loading states. The computations were mainly based on the analytic solutions for this problem using Gauss–Chebyshev quadrature to achieve the integration which is singular at the integral boundary. The crack extension resistance curves in terms of stress intensity (K_R-curves) were determined by combining the crack initiation toughness that is the inherent toughness of the material needed to resist the crack initiation in the case that is in the lack of an extension of the main crack with the contribution due to the cohesive force along the fictitious crack zone during the complete processes of fracture. The situation of crack propagation can be judged by comparing K_R-curves of crack extension resistance with the stress intensity factor curves which were calculated using the lengths of the extending crack and the corresponding loads at each loading states, e.g., when the crack extension resistance curve(K_R-curve) is lower than the stress intensity factor curve, the crack propagation is stable; otherwise, it is unstable. In the computation, the obtained relationship between the crack tip opening displacement CTOD and the amount of crack extension for the complete fracture process is in agreement with the testing results of other researchers. This revised version was published online in August 2006 with corrections to the Cover Date.     

基于内高压成形方法的航空发动机空心叶片工艺设计

目的成形精度更高、质量更好的航空发动机钣金空心叶片。方法对空心叶片的结构进行分析,设计出了一种带有刚性凸模的内高压成形方法。根据塑性变形理论分析了零件的受力状况,根据所制定的工艺路线建立了有限元模型,对成形过程中的不同的管坯直径、内压大小、刚性凸模尺寸等工艺参数进行了仿真。结果得到了成形空心叶片的最优的工艺路线和工艺参数,有效抑制了零件的过度减薄和回弹等现象。结论通过此带有刚性凸模的内高压成形方法,可以很好地实现该零件的虚拟成形。     

表面淬火等离子体束温度及宽度测量方法

等离子体表面淬火技术是一种新型表面处理技术。该技术通过等离子体发生器产生高能等离子体束作用于金属材料表面,使材料表面温度快速升高超过相变温度,再依靠自身快速冷却达到淬火效果。目前在缺少对淬火过程中等离子体束温度的测量方法。本文研究出一种数字图像处理与双色比色法相结合的方法能够测量出等离子体束在表面淬火过程中的温度。实验结果显示本方法可以有效观测到淬火过程中的等离子体束温度与宽度及其变化,为等离子体表面淬火技术提供了支持。     

Study on Fracture Behaviour of a Polymer‐Bonded Explosive Simulant Subjected to Uniaxial Compression Using Digital Image Correlation Method

Abstract: Quasi‐static uniaxial compression experiments were conducted on a polymer‐bonded explosive (PBX) simulant. At macro‐scale, the deformation and fracture process of samples were recorded using a charge‐coupled‐device camera. Microscopic examination was conducted to in situ observe the deformation and fracture processes of samples using SEM equipped with a loading stage. Microscopic damage modes, including interfacial debonding and particle fracture, were observed. The digital image correlation (DIC) technique was used to calculate the recorded images, and the macro‐ and micro‐scale displacement and strain fields were determined. Crack initiation, crack propagation, fracture behaviour and failure mechanism of samples were studied. The effects of aspect ratios on fracture behaviour and failure mechanism of PBX simulant were analysed.     

不同冲击载荷下水中砼破坏机理的初步研究

在水中爆炸冲击载荷的作用下,混凝土的动态响应和破坏模型与在地面上有很大的不同,加载应用率大小和作用历史对混凝土破坏历程有着更复杂的影响,冲击超压不是决定发生破坏的唯一因素,对此采用不同种类炸药,进行不同压力峰值和作用历史的爆炸载荷冲击实验,并初步提出了水中混凝土的动态破坏模型,给出了混凝土材料的临界破坏条件。     

Smoothing Measured Displacements and Computing Strains Utilising Finite Element Method

Abstract: A method for smoothing measured displacements and computing strains utilising finite element and least‐squares methods is proposed. Nodal displacement values of a finite element model are determined by fitting the interpolation functions of elements to measured displacement values using the method of least‐squares. The displacements in the region where the measurement values are not obtained or unreliable are determined by solving finite element equations. Then, strains are obtained using a displacement‐strain relationship. The validity is demonstrated by applying the proposed method to the displacement distributions of a plate with a hole obtained using finite element method and those around a crack tip obtained using digital image correlation. Results show that the displacements and the strains can be determined accurately by the proposed method. Furthermore, the strains near free boundaries and strain concentration region can be computed. As strains can be evaluated easily and accurately, the proposed method can be used as one of the data processing methods for optical methods.     

Modelling the Effects of Geometric Imperfections on the Buckling and Initial Post‐buckling Behaviour of Flat Plates Under Compression Using Measured Data

Abstract: Recent developments in optical techniques have allowed accurate representations of the geometry of test specimens to be obtained. These enable the nature of geometric imperfections resulting from manufacture or set‐up to be captured in a form which allows them to be incorporated directly into models generated to predict the behaviour of the structure. This study examines the effect of such imperfections on the behaviour of a series of panels, simply supported along all four edges, and subject to uniaxial compressive in‐plane loading. In each case, digital image correlation is used to determine the initial profile and set‐up of the panel and to monitor its behaviour during test. The data are used to automatically generate a series of meshes representative of each of the specimens tested, suitable for finite element analysis. Comparison of the results obtained from these analyses with those found during the experiments modelled shows an improved correlation when compared with standard techniques for assessing imperfection sensitivity. Set‐up is straightforward, and models can be obtained quickly based on the data collected.     

Experimental Investigations on Deformation and Fracture Behavior of Glass Sphere Filled Epoxy Functionally Graded Materials

In this paper, deformation and fracture behavior of glass sphere filled epoxy functionally graded materials (FGM) are numerically evaluated and experimentally studied. The fabrication of the FGM is described in detail, and the spatial gradation of elastic modulus and the microscopic structure in FGM are measured and analyzed. The deformation and fracture characterization of the FGM specimen with a crack oriented along the direction of the elastic gradient under three point bend are studied by the experimental and the finite element method. The influences of crack location at both the stiff and the compliant sides of the FGM specimen on crack initiation, deformation field and stress intensity factor are analyzed. The results are: (a) The neutral-axis in the FGM specimen under three-point-bending will shift toward the stiffer side; (b) The initial fracture load increases with the increase of elastic modulus at the crack tip; (c) The elastic gradients shield a crack on the compliant side and lower the stress intensity factor when compared to the one with crack on the stiff side. These results will be useful for better design and reliable evaluation of FGM.