Loading‐rate dependence of mode I crack growth in concrete

Mode I crack propagation process of concrete under relatively low loading rates which cover four orders of magnitude (0.2 μm/s to 2.0 mm/s) is investigated with three‐point bending (TPB) beams. All measured material properties exhibit rate sensitivity and follow a log‐linear relationship with the loading rate. A rate‐sensitive softening curve is established. The complete load‐crack mouth opening displacement (P‐CMOD) curve, crack propagation length, and fracture process zone (FPZ) length are simulated based on crack growth criterion with the fitted material parameters under those loading rates. Results show that the simulated P‐CMOD curves agree well with those of experimental measurements. It is clear that the peak load increases with the loading rate and so is the critical crack mouth opening displacement. Moreover, under the same load level, the length of the FPZ and the cohesive stress at the initial crack tip also increase with the increasing loading rate.     

Effect of acid corrosion on crack propagation of concrete beams

The effect of acid corrosion on crack propagation of concrete beams was theoretically studied by the method of crack extension resistance curve. Based on this method, a calculation approach was proposed to determine fracture stress intensity factors in crack propagation of concrete beams. Loop iteration analysis was carried out to calculate maximum bearing capacity load, unstable crack toughness, resistance toughness curve, cohesive toughness curve and load–crack mouth opening displacement. Both bilinear and nonlinear softening traction–separation curves were adopted for each of these calculation parameters. The analysis results of each showed the effect of acid corrosion degrees. The influence of acid corrosion on fracture properties was discussed through the calculated results of cohesive toughness curves. These five kinds of simulated results were basically consistent, before the load attained the maximum value. However, with further crack propagation, cohesive toughness of nonlinear softening model was significantly larger than that of bilinear softening model, and the descending branch of P–CMOD curve by nonlinear law is higher than that by bilinear law. To validate the approach, tests of specimens under six different corrosion periods were experimentally studied, using three-point bending notched concrete beams soaked in sulphuric acid solution. The Double-K fracture parameters were investigated based on the test results, and load–crack mouth opening displacement curves for different acid conditions were obtained using synchronous sampling of a load sensor and clip-gauge. Numerical results by bilinear softening model showed a good correlation with the experimental ones.     

岩石-混凝土界面拉伸断裂性能的率相关性研究EI北大核心CSCD

该文弯曲断裂试验获得了不同应变率下界面的抗拉强度、荷载-加载点位移曲线、荷载-裂缝口张开位移曲线、起裂荷载和峰值荷载,通过夹式引伸计法和DIC法获得了临界裂缝扩展长度。并计算了界面断裂能及双K断裂参数,分析了不同应变率下界面断裂过程区演化规律及特征长度的变化。结果表明:随应变率的增大,断裂能和起裂韧度增大,临界裂缝长度和失稳韧度先增加后减小,断裂过程区长度及特征长度随应变率的提高而减小。该文从裂缝发展路径、自由水粘性、惯性效应三方面探讨了岩石-混凝土界面断裂参数的率效应。     

COHESIVE MODELLING OF PROCESS REGIONS FOR CRACKS IN LINEAR ELASTIC STRUCTURES—FUNDAMENTAL ASPECTS

The process region at the tip of a crack in a linear elastic structure has been modelled by a cohesive zone. Growth of the front end of the cohesive zone is governed by a critical stress intensity factor criterion, and advance of the original traction free crack is determined by a critical crack opening at the rear end of the cohesive zone. Damage resistance curves relating the applied stress intensity factor to the growth of the cohesive zone have been calculated for an idealized structure containing two characteristic dimensions. Instability resulting in failure of the structure is found to occur either by unstable growth of the front end of the cohesive zone, without a fully developed cohesive zone, or by unstable growth of the original flaw, when the crack opening displacement at the rear end of the cohesive zone reaches a critical value. The influence of the size of the structure compared to the length of the cohesive zone is investigated, and conditions for the limits of validity of the small scale yielding assumption are discussed. Comparisons are made between the maximum load and the length of the cohesive zone at instability resulting from the present analysis, and the values predicted by linear elastic fracture mechanics.     

Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

Crack Growth Across a Strength Mismatched Bimaterial Interface

Crack growth across an interface between materials with different strength is examined by a cohesive zone model. The two materials have identical elastic properties but different fracture process properties, or different yield stresses, which is modeled by different cohesive stresses. The fracture criteria is a critical crack opening displacement. Load is represented by a stress intensity factor defining a remote square root singular stress field. The results show that the ratio between the cohesive stresses of the two materials primarily determines the behavior of the critical stress intensity factor. When the crack approaches a material with a higher cohesive stress the crack tip is shielded, but if the crack approaches a material with smaller critical crack opening displacement the maximum level of shielding is determined by the ratio between the critical crack opening displacements. When a crack approaches a material with a lower cohesive stress it is exposed to an amplified load. This revised version was published online in August 2006 with corrections to the Cover Date.     

A cohesive edge crack

The nucleation and growth of a cohesive edge crack is studied. This topic is germane to the initiation and early stage of crack growth during unnotched beam testing, the growth of short edge cracks in finite test pieces, and the formation of tension cracks of geological origin. This paper focuses on an edge crack in a semi-infinite plane, under a uniform far-field tensile stress acting parallel to the plane boundary. Expressions for the Mode I stress-intensity-factor and crack-opening-displacement for an edge crack subjected to arbitrary crack face loading are determined via the weight function method. All of the constants needed to define the weight function and associated integrals are themselves explicit functions of just two constants: f_r and ψ. Two types of softening behavior in the cohesive zone are examined: rectangular softening, and linear softening. In each case the process zone size, energy-release-rate, crack-opening displacement and load-ratio are examined. The different test behavior exhibited under load-control versus fixed-grip displacement control is explored. The test control conditions alter the fracture behavior significantly. For a linear softening cohesive edge crack, it is found out that under fixed-grip control (load-control), the process zone size decreases (increases) steadily with increasing traction-free crack length, approaching the semi-infinite crack asymptote from above (below). The differences between load-control versus fixed-grip control decrease rapidly with increasing traction-free crack length.     

Process zone analysis for the single-edge notched specimen: Part I. Process zone size and crack profile

A systematic analysis of the process zone is presented. Relations among the process zone size, load and crack opening displacement (COD) are derived using the weight function method and a power function closing pressure distribution in the process zone. These relations are specialized and used to study the behaviour of the single-edge notched (SEN) specimen loaded in tension and in bending. This study shows that the method presented here may be successfully used to analyze the fracture of finite-size specimens.     

Fracture analysis of Kevlar-49/epoxy and e-glass/epoxy doublers for reinforcement of cracked aluminum plates

Adhesively bonded composite patch repair is efficient means to regain load carrying capacity, alleviate the crack growth, and improve the service life of the damaged structure. In this paper, three dimensional finite element models are developed to examine the fracture behavior of a single edge V-notched Aluminum plate repaired with Kevlar-49/epoxy or e-glass/epoxy pre-preg patches on both sides. Contour integral method was used for evaluating the stress intensity factor (SIF), an indicator of the crack stability. The load transfer mechanisms, stress distribution, damage variable (D), and crack mouth opening displacement (CMOD), were also presented to estimate the effectiveness of composite patch repair. The influence of the patch material, crack length and the adhesive thickness has been investigated. Results have shown that the crack induced damage increased nonlinearly with a larger crack size. With the composite patch repairs, SIF is reduced to 1/7–1/10 of that of the bare plate and CMOD decreased by 79%. The damage variable is reduced significantly and the load capacity is increased. A thinner adhesive layer results in a higher percentage of load shared by the composite patch.     

Experimental determination of fracture parameters for crack propagation in hardening cement paste and mortar

For all cement-based composite materials, hardening cement paste and mortar are the matrix materials. Their fracture properties are the basis for studying the fracture characteristic of cement-based composite materials. Therefore, three-point bending beams with three different sizes and three different strengths were tested to study the basic fracture properties of hardening cement paste and mortar. Corresponding values of load (P), crack mouth opening displacement (CMOD), and loading point displacement (δ) were simultaneously recorded. The initial cracking load P _ini was determined by using resistance strain gauges making up a full-bridge circuit, and the crack propagation process was observed during the test. It was found that the fracture behavior of both hardening cement paste and mortar are not brittle fracture and show a steady crack propagation process before the peak load was reached. This means that the fracture behaviors of all cementitious composites are nonlinear, even hardening cement paste and mortar. Therefore, corresponding fracture parameters of the hardening cement paste and mortar were determined using the double-K fracture model. The results indicate that this model is applicable to hardening cement paste and mortar. In addition, according to the principle of work of fracture, fracture energy values of the tested hardening cement paste and mortar were calculated after taking into account the contribution of the tail of the P–δ curve on fracture energy.     

Observation of fracture process zone by laser speckle technique and governing mechanism in fracture of concrete

Fracture tests with a wedge-loading device are carried out on mortar and concrete specimens so as to have stable crack growth. Using laser speckle technique the length of macrocrack and the distribution of crack opening displacement are measured. Results are compared with those obtained by the boundary element method (BEM) analysis for a Dugdale-Barenblatt-type model of a fracture process zone. The governing mechanism in fracture of concrete and the mechanism which is represented by the model are discussed with special attention to the microcracking zone. It is deduced that a Dugdale-Barenblatt-type model does not represent the microcracking zone, thus implying that the microcracking zone and the bridging zone correspond to the pre-peak nonlinear part of the stress-strain curve in a uniaxial tension test and the post-peak tension-softening curve, respectively. It is concluded that the effect of microcracking on the maximum load is less significant than that of bridging. Possible models which include the effect of microcracking in addition to that of bridging are proposed.     

Limiting Equilibrium of a Cracked Body with Regard for the Specific Features of the Distribution of Stresses Near the Crack Tip

By using the well-known δ _c -model, we establish new formulas for the evaluation of the crack-tip opening displacement with regard for a more complicated interaction of the edges of a model cut in the process zone of the material and determine the dependence of the critical load on the ratio of the initial crack length to the length of the process zone regarded as constant. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 4, pp. 5–8, July–August, 2005.     

混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

Understanding fatigue crack propagation in AISI 316 (N) weld using Elber’s crack closure concept: Experimental results from GCMOD and acoustic emission techniques

An experimental study of fatigue crack propagation and crack closure behaviour, in compact tension specimens of AISI 316 (N) weld has been conducted. The crack closure load was determined from the changes in the slope of the load–displacement curves using global crack mouth opening displacement (GCMOD) type gauge. The results were compared with those measured by acoustic emission technique which showed good agreement with each other. The experimental data bear clear evidence of fatigue crack closure. The crack opening force was found to increase moderately with crack length and increasing R-ratio, under a constant P_max of 5 kN. Above a critical R-ratio of 0.45 (approximately), the crack closure load is smaller than the minimum applied load. A good correlation was obtained for ΔK_eff/ΔK = 0.6684 – 2.4135R + 7.0077R² in the range 0 R  0.5. The magnitude of crack closure is used to interpret observed crack growth behaviour at different R-ratios.     

EFFECT OF ELASTIC MISMATCH ON THE GROWTH OF A CRACK INITIALLY TERMINATED AT AN INTERFACE IN ELASTIC PLASTIC BIMATERIALS

Abstract A crack perpendicular to, and initially with the tip on, a bimaterial interface is studied. An asymptotic analysis is performed and crack growth proceeds straight ahead at constant remote load. Mode I conditions and plane strain are assumed. The materials on both sides of the interface are elastic perfectly-plastic with different elastic properties and the same yield stress. A finite element analysis is made and crack growth is simulated by an element relaxation technique. Because of the interface, the crack-tip driving force is not constant, which is reflected in the near-tip state. The development of the plastic zone and the crack opening displacements is presented for different elastic mismatches. Small scale yielding like results are obtained after a crack extension of about the plastic zone size from the interface, i.e. long before a square-root singular stress field may be expected to embed the plastic zone. An important observation is that the development of the crack opening displacement at the initial stage of growth is reversed when plasticity is introduced, as compared to the prediction by an elastic model. A region of stable crack growth is identified at the initial phase of growth into a stiffer material, solely due to elastic mismatch.     

CTOD-R curve construction from surface displacement measurements

The construction of a fracture resistance δ–R (or J–R) curve requires the appropriate measurement of crack-tip opening displacement (CTOD) as a function of crack extension. This can be made by different procedures following ASTM E1820, BS7448 or other standards and procedures (e.g., GTP-02, ESIS-P2, etc.) for the measurement of fracture toughness. However, all of these procedures require standard specimens, displacement gauges, and calibration curves to get intrinsic material properties. This paper deals with some analysis and aspects related to the measurement of fracture toughness by observing the surface of the specimen. Tests were performed using three-dimensional surface displacement measurements to determine the fracture parameters and the crack extension values. These tests can be conducted without using a crack mouth opening displacement-CMOD or load-line displacement gauge, because CMOD can be calculated by using the displacement of the surface points. The presented method offers a significant advantage for fracture toughness testing in cases where a clip gauge is not easy to use, for example, on structural components. Simple analysis of stereo-metrical surface displacements gives a load vs. crack opening displacement curve. Results show that the initiation of stable crack propagation can be easy estimated as the point of the curve’s deviation. It is possible to determine the deviation point if the crack opening displacement measurements are close to crack tip in the plastic zone area. The resistance curve, CTOD-R, is developed by the local measurement of crack opening displacement (COD) in rigid body area of specimen. COD values are used for the recalculation with the CMOD parameter as a remote crack opening displacement, according to the ASTM standard.     

Viscoelastic Creep Crack Growth: A Review of Fracture Mechanical Analyses

The study of time dependent crack growth in polymers using a fracture mechanics approach has been reviewed. The time dependence of crack growth in polymers is seen to be the result of the viscoelastic deformation in the process zone, which causes the supply of energy to drive the crack to occur over time rather than instantaneously, as it does in metals. Additional time dependence in the crack growth process can be due to process zone behavior, where both the flow stress and the critical crack tip opening displacement may be dependent on the crack growth rate. Instability leading to slip-stick crack growth has been seen to be the consequence of a decrease in the critical energy release rate with increasing crack growth rate due to adiabatic heating causing are duction in the process zone flow stress, a decrease in the crack tip opening displacement due to a ductile to brittle transition at higher crack growth rates, or an increase in the rate of fracture work due to more rapid viscoelastic deformation. Finally, various techniques to experimentally characterize the crack growth rate as a function of stress intensity have been critiqued. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crack growth in cement-based composites

A model that can be used to predict Mode I crack growth in cement-based composites is presented. The region ahead of a crack tip, where nonlinear deformations and aggregate interlock occur, is modeled as an extension of the actual stress-free crack subjected to a closing pressure that depends on the crack face displacements. In the case of concrete, crack propagation is assumed to occur when the crack opening displacement at the tip of the actual crack reaches a critical value. To predict results, the elastostatics problem of a layer containing a vertical edge crack was solved using a Green's function approach together with integral transform techniques. Stress intensity factors and crack opening displacements were obtained by numerically solving a singular integral equation. The closing pressure function and critical crack tip opening displacement were taken from experimental data for various materials, and the model was applied to the analysis of experiments performed on initially notched concrete and fiber-reinforced mortar beams.     

基于虚拟裂缝模型的混凝土断裂过程区研究

利用虚拟裂缝模型对混凝土断裂过程区进行了研究.以无限大板中心拉伸裂缝模型为例,将过程区裂缝张开位移采用多项式级数形式表示,求得了断裂过程区上的位移分布和粘聚力分布.进而分析了材料参数对断裂过程区上的位移、粘聚力、断裂过程区长度以及峰值外荷载的影响.结果表明：断裂过程区上的位移和粘聚力均为非线性分布.断裂过程区长度随骨料最大粒径增大而逐渐增大,随抗压强度增大而逐渐减小.峰值外荷载随骨料最大粒径和抗压强度增大均逐渐增大.