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.     

基于随机骨料模型的EPS混凝土粒子尺寸效应分析

建立基于随机分布的EPS混凝土细观力学模型,对EPS混凝土的受压损伤破坏过程进行数值模拟,分析EPS混凝土的损伤破坏过程。研究表明,EPS混凝土的损伤破坏有两种形态,即延性破坏和脆性破坏。延性破坏与EPS颗粒的面积占有率、断裂过程区长度有关;脆性破坏与EPS颗粒的面积占有率、粒径大小以及颗粒间距有关。在EPS颗粒面积占有率较低的情况下,EPS混凝土的粒子尺寸效应对混凝土力学性能的影响较明显,在较高面积占有率的情况下,粒子尺寸效应对其影响较小。随着EPS颗粒面积占有率的增加,EPS混凝土损伤破坏由脆性破坏向延性破坏转变。建立基于损伤力学与断裂力学的粒子尺寸效应数学模型,用数值模拟进行验证,发现两者吻合较好。     

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.     

基于DIC技术的沥青混合料断裂特性实验研究

开裂是钢桥面铺装层的主要破坏形式。为研究钢桥面沥青混合料断裂特性及裂纹扩展规律,通过小梁三点弯曲实验,应用数字图像相关方法(DIC)图像采集系统采集试件从加载到破坏的全过程图像。利用非接触式全场应变测量系统(VIC-2D)计算试件在加载过程中的位移场和应变场,并分析出裂缝萌生、发展的规律。结果表明:沥青混合料从相对较弱的胶浆区或胶浆-粗集料界面区开裂和发展;当胶浆-粗集料界面与裂纹发展方向垂直时,粗集料对裂纹的发展有阻断作用;胶浆裹覆细集料的运动轨迹与胶浆的运动轨迹一致。     

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.     

数字图像技术在航空铝合金形变测量中的应用

利用DIC(Digital image correlation)非接触全场应变测量系统分析2024铝合金板材静态拉伸应变场。对散斑质量参数、图像采集系统参数进行正交试验优化。优化结果表明,影响散斑质量的主次因素及最优结果分别为:散斑半径0.02in,散斑密度50%,散斑分布随机性69%;影响图像采集系统的主次因素及最优结果分别为:子集大小59个像素,步长值12个像素,相机间的角度20~25°,光圈值5.6~8。采用该优化参数测量无孔及不同开孔尺寸铝合金板材静态拉伸应变场。首先,对无孔试样裂纹两侧取点,研究裂纹扩展趋势,判定裂纹源及相应载荷。其次,研究长短轴之比及开孔面积对力学性能的影响,并沿孔径方向取点,分析局部应变情况。研究表明,越靠近开孔位置,应变越集中。减小开孔面积,降低开孔的长短轴之比,可以有效降低试样的应变集中系数,延长使用寿命。最后,对比分析非接触测量方法、引伸计法及Patran建模仿真方法试验结果。     

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.     

Comparison of the identification performance of conventional FEM updating and integrated DIC

Full‐field identification methods are increasingly used to adequately identify constitutive parameters to describe the mechanical behavior of materials. This paper investigates the more recently introduced one‐step method of integrated digital image correlation (IDIC) with respect to the most commonly used two‐step method of finite element model updating (FEMU), which uses a subset‐based DIC algorithm. To make the comparison as objective as possible, both methods are implemented in the most equivalent manner and use the same FE model. Various virtual test cases are studied to assess the performance of both methods when subjected to different error sources: (1) systematic errors, (2) poor initial guesses for the constitutive parameters, (3) image noise, (4) constitutive model errors, and (5) experimental errors. Results show that, despite the mathematical similarity of both methods, IDIC produces less erroneous and more reliable results than FEMU, particularly for more challenging test cases exhibiting small displacements, complex kinematics, misalignment of the specimen, and image noise. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Structural integrity assessment of nuclear containment through fracture characterization

The paper deals with the study of structural response of partially cracked nuclear containment model structure in over pressurized condition with the simulated experiments conducted under severe accidents analysis program for Indian nuclear containment structures. In this research, the fracture characterization of concrete containment structure is also investigated through the over pressure experiments on the BARC Containment (BARCOM) test model structure, which represents 1:4 scale of the prototype 540 MWe Tarapur pre‐stressed nuclear containment structure. In addition to the surface‐type electrical resistance, strain gauges conventionally and commonly deployed for containment proof‐test and ultimate load capacity evaluation of containment models, embedded vibratory wire strain gauges (VWSGs), the digital image correlation (DIC) technique, and soap bubble tests are employed in this study. For fracture characterization, an optical crack profile (OCP) technique is developed through DIC full‐field experiment conducted at the identified critical locations with conventional strain gauges to evaluate the fracture energy and the characteristics of the fracture process zone of concrete containment model structure subjected to the over‐pressure condition for its performance assessment in the case of the beyond design basis accidents. The combination of conventional sensors and full‐field DIC deployed for the first time on the largest scale containment model along with the associated analysis is shown to be effective in fracture characterization and improved structural integrity assessment of the containment model.     

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.     

Measurement of discontinuous displacement/strain using mesh-based digital image correlation

In this study, a method for evaluating discontinuous displacement and strain distributions using digital image correlation (DIC) is proposed. A finite element mesh-based DIC method is used for measuring displacements while taking into account displacement and strain discontinuities. Smoothed displacements are thus obtained, and strains are computed from the measured displacements using the finite element mesh again. Discontinuous strains can be obtained by the proposed method using a split finite element mesh. The effectiveness of this method is validated by applying it to measure the displacement and strain in a triaxially woven fabric composite containing numerous free boundaries, to measure displacements around a crack and the displacement and strain around the interface between dissimilar materials. Results show that the discontinuous displacement and strain distributions can be measured by the proposed method. The proposed method is expected to be applicable for the experimental evaluations of various structures and members, including displacement and strain discontinuities such as free boundaries, cracks, and interfaces.