聚丙烯纤维水泥稳定碎石断裂性能试验研究

通过30个尺寸为100mm×100mm×515mm的聚丙烯纤维水泥稳定碎石和普通水泥稳定碎石三点弯曲试件断裂试验,探讨了聚丙烯纤维对水泥稳定碎石断裂韧度(KIC)、断裂能(GF)、临界裂缝嘴张开位移(CMODC)、临界裂缝尖端张开位移(CTODC)、极限裂缝嘴张开位移(CMODmax)和极限裂缝尖端张开位移(CTODmax)的影响。试验结果表明:聚丙烯纤维的掺入可增大水泥稳定碎石的断裂韧度、断裂能、临界裂缝嘴张开位移、极限裂缝嘴张开位移、临界裂缝尖端张开位移和极限裂缝尖端张开位移;随着聚丙烯纤维体积掺量的增加,断裂韧度、临界裂缝嘴张开位移和临界裂缝尖端位移的变化无明显规律,但断裂能、极限裂缝嘴张开位移和极限裂缝尖端位移基本上呈线性增加的。     

Effect of loading condition,specimen geometry,size-effect and softening function on double-<Emphasis Type="BoldItalic">K</Emphasis> fracture parameters of concrete

This paper presents numerical investigation of the influence of the specimen geometry, loading condition, size-effect and softening function of concrete on double-K fracture parameters. The input data needed for computation of the double-K fracture parameters are obtained from the well-known version of Fictitious Crack Model (FCM). FCM is developed for three standard specimens: three-point bend test, compact tension specimen and four-point bend test of size range 100–600 mm at relative size of initial crack length 0.3. The analysis of numerical results shows some interesting behaviour of double-K fracture parameters.     

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.     

Study of elastic-plastic fracture toughness determination

The elastic-plastic fracture toughness viaJ-integral and crack tip opening displacement (CTOD) has been obtained in two structural steels using several fitting equations representing the resistance curve of the material. The toughness is determined as the values corresponding to the critical stretched zone width (SZW) on theR-curves and with respect to 0.2 mm crack growth. The SZW measurements were performed by scanning electron microscopy. The various toughness values have been compared and the importance of using appropriateR-curves based on physical considerations has been pointed out. TheJ-CTOD relationship during the blunting process has been experimentally investigated from load-displacement records of the fracture test.     

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.     

A simplified method for determining double-K fracture parameters for three-point bending tests

A simplified method for determining the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor K _I ^c caused by the cohesive force (x) on the fictitious crack zone for three-point bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters K _Ic ⁱⁿⁱ and K _Ic ^un. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.     

小尺寸混凝土试件双K断裂参数试验研究

采用最大尺寸为680mm×160mm×40mm的标准三点弯曲梁试件,利用在初始裂缝两侧粘贴电阻应变片并利用混凝土裂缝扩展到此处时其应变回缩的方法测得了起裂荷载Pini,在此基础上根据Pini及初始缝长a0得到了起裂断裂韧度KIiCni;根据在试验中测得的最大荷载Pmax及对应的裂缝口张开位移CMODC计算了混凝土等效裂缝长度aC,据此计算了失稳断裂韧度KIuCn。结果表明:采用电阻应变片法可准确测定混凝土的起裂荷载Pini,且方法简单。试验结果还表明:在本试验范围内,三点弯曲梁法测得的混凝土双K断裂参数KIiCni、KIuCn与试件高度无关,进一步说明了混凝土双K断裂参数可以作为描述混凝土裂缝扩展的断裂参数。     

Rate-dependent fracture toughness of pure polycrystalline ice

A series of three-point bend tests using single edge notched testpieces of pure polycrystalline ice have been performed at three different temperatures (–20°C, –30°C and –40°C). The displacement rate was varied from 1 mm/min to 100 mm/min, producing the crack tip strain rates from about 10^–3 to 10^–1 s^–1. The results show that (a) the fracture toughness of pure polycrystalline ice given by the critical stress intensity factor (K _IC) is much lower than that measured from the J—integral under identical conditions; (b) from the determination of K _IC, the fracture toughness of pure polycrystalline ice decreases with increasing strain rate and there is good power law relationship between them; (c) from the measurement of the J—integral, a different tendency was appeared: when the crack tip strain rate exceeds a critical value of 6 × 10^–3 s^–1, the fracture toughness is almost constant but when the crack tip strain rate is less than this value, the fracture toughness increases with decreasing crack tip strain rate. Re-examination of the mechanisms of rate-dependent fracture toughness of pure polycrystalline ice shows that the effect of strain rate is related not only to the blunting of crack tips due to plasticity, creep and stress relaxation but also to the nucleation and growth of microcracks in the specimen.     

Crack tip reinforcement by bridging elements: modelling the fracture of the matrix material

There is a wide range of physical situations where the faces of a crack in a matrix material with limited ductility are restrained from opening, a phenomenon known as crack reinforcement. In quantifying this phenomenon, the simplest way of modelling the behaviour of the matrix material ahead of a crack tip is to assume that it deforms in accord with the laws of linear elasticity with the crack extending when the stress intensity at the crack tip (the leading edge of the restraining region) attains a critical value,K _IC, the fracture toughness of the matrix material; i.e. the details of the matrix deformation and fracture behaviour are ignored. The viability of thisK-matrix assumption is examined for the case of a semi-infinite crack in a remotely loaded infinite solid, for which the restraining stress between the crack faces increases linearly with crack opening until the attainment of a critical opening when the restraining stress falls to zero. The analysis defines the range of material parameters for which theK-matrix assumption is adequate with regard to the determination of (a) the applied value ofK required for the crack tip and restraining zone to propagate through the solid, and (b) the size of the restraining zone when propagation occurs. TheK-matrix assumption always gives an overestimate of the appliedK, but the overestimation is small when the matrix toughness contribution is small or is dominant. However, when the contributions from the matrix toughness and the toughness provided by the restraining material are roughly equivalent, theK-matrix assumption leads to a significant overestimate of the appliedK, and in this situation the matrix material behaviour should be modelled more precisely.     

Effect of polypropylene fiber on fracture properties of cement treated crushed rock

A parametric experimental study has been conducted to investigate the effect of polypropylene fibers on the fracture properties of cement treated crushed rock (CTCR), which is a new pavement composite material. By means of three-point bending method, the fracture toughness, fracture energy, the ultimate deflection in span center, critical crack mouth opening displacement, critical crack tip opening displacement, maximum crack mouth opening displacement and maximum crack tip opening displacement of the specimen of CTCR reinforced with polypropylene fibers were measured respectively. The test results indicate that the addition of polypropylene fibers is helpful to improve the fracture properties of CTCR. Polypropylene fibers have great improvement on the fracture parameters of CTCR. Besides, the fracture parameters increase gradually and the fracture relational curves are becoming plumper and plumper when the fiber volume fraction increases from 0% to 0.1%. Furthermore, the capability of polypropylene fiber to resist crack propagation of CTCR appears to be becoming stronger and stronger with the increase of fiber volume fraction with the fiber volume fraction not beyond 0.1%.     

Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams

In this paper, an attempt is made to determine the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un using three-point bending notched beams. First, based on the knowledge from extensive investigations which showed that the nonlinearity of P-CMOD curve is mainly associated with crack propagation, a linear asymptotic superposition assumption is proposed. Then, the critical effective crack length a is analytically evaluated by inserting the secant compliance c into the formula of LEFM. Furthermore, an analytical result of a fictitious crack with cohesive force in an infinite strip model was obtained. The double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un as well the critical crack tip opening displacement CTOD_c were analytically determined. The experimental evidence showed that the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un are size-independent and can be considered as the fracture parameters to describe cracking initiation and unstable fracture in concrete structures. The testing method required to determine K _Ic ⁱⁿⁱ and K _Ic ^un is quite simple, without unloading and reloading procedures. So, for performing this test, a closed-loop testing system is not necessary.     

The Identification of a Hidden Long‐Term Plastic Damage Stage During Splitting Tensile Loading of Concrete: A Fracture Mechanics Approach

Abstract: A new method for the determination of fracture toughness K_IC, fracture energy G_F and critical crack tip opening displacement CTOD_c of mortars and concretes with maximum size of aggregates up to 8 mm is presented. This was achieved by using a suitable modification of the conventional splitting tensile test. The values that were obtained are in accordance with those of other researchers. On the basis a clear‐cut fracture mechanics analysis, we extract a set of equations that correlates the above quantities with the crack rate. Specific plastic damage stages that accompany the crack growth were thus easily identified. A pre‐peak damage process of a characteristic bandwidth of 0.1–1 μm and length from a few micrometres to a few millimetres appears first. Damage process of this kind can be diffused and dispersed in bulk of the loading component or it can also be localised and formed into an active attractor cracking path through its chain accumulation. Then another damage stage, coming directly through the formation of the well‐known fracture process zone near the crack tip of 10 μm in bandwidth and a few tens of millimetres in length, must be added. Finally, a large‐scale stage involving the influences of composition and texture of stressed components as well as their loading and geometry conditions must be superimposed on the first two. This third damage process comes directly through the reordering and redistribution of the aforementioned features, during the evolution of fracture, giving an effective length that varies from few tens of millimetres to some metres. All these effective lengths could easily be extracted from the calculated concrete fracture quantities.     

Evaluation of Fracture Parameters by Double-G,Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (K_Ic^c), unstable fracture toughness (K_Ic^un) and initiation fracture toughness (K_Icⁱⁿⁱ) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K_Ic^un of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.     

THE EFFECTS OF CRACK DEPTH ON THE J-INTEGRAL AND CTOD FRACTURE TOUGHNESS FOR WELDED BEND SPECIMENS

This work deals with the influence of crack depth on the fracture toughness at initiation of crack growth and the constraint factor in relationship between the J-integral and the crack tip opening displacement (CTOD). A series of tests were performed on high strength low alloyed HT80 steel welds, and the critical J-integral and CTOD were determined using the load versus load point displacement record from three-point bend specimens with 0.05 < a/W < 0.5. It was found that the fracture toughness for shallow cracks at the onset of crack growth was larger than that for deep cracks for the steel welds tested, but it is felt that there is no fixed relationship between these values in the welds tested. The constraint factor is also a function of crack depth, and values of the factor increase from 0.5 to 1.5 when a/W increases from about 0.05 to 0.5. The factors are not very sensitive to the crack tip materials (HAZ or weld metal) in the welds tested.     

Fracture assessment of damaged square hollow section (SHS) K-joint using BS7910:2005

A pre-cracked square hollow section K-joint was tested under static loads up to failure. It is found that the load-displacement curves are in good agreement with the finite element results. Ductile tearing was observed to initiate from the crack front parallel to the chord side wall where fracture toughness is smaller. Using plastic collapse load obtained via twice elastic compliance technique and fracture toughness obtained from crack tip opening displacement, the two fracture parameters K_r and L_r are plotted on the standard failure assessment diagram. It shows a conservative assessment for the cracked K-joint subjected to brace end axial loads.     

采用峰值荷载法确定全级配水工混凝土断裂参数

该文采用峰值荷载法研究了全级配水工混凝土试件的断裂参数。通过有限元方法,得到了适用于全级配水工混凝土的非标准楔入劈拉试件的应力强度因子K、裂缝嘴张开口位移CMOD计算公式以及裂缝张开位移COD与CMOD比值COD/CMOD的相关曲线。基于相关断裂试验,通过该文所提公式得到了全级配水工混凝土的等效断裂韧度与临界裂缝尖端张开口位移CTOD_c等断裂参数。研究结果表明:峰值荷载法可应用于截面尺寸不同而缝高比相同的全级配水工混凝土试件,峰值荷载法只需实测各试件的峰值荷载,就可方便确定全级配水工混凝土的断裂参数。     

A new expression for crack opening stress determined based on maximum crack opening displacement under tension–compression cyclic loading

The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension–compression loading cycles. Based on elastic–plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN ? ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.     

Crack-Tip Toughness From Wide-Range COD Measurements

An evaluation of crack opening displacement measurements is presented, which enables the determination of the crack tip toughness K ₁₀ from the whole database. The procedure is applied to results from literature for coarse-grained and fine-grained alumina.     

POP-IN AND CRACK ARREST IN AN HY80 WELD

It is generally thought that, when a material is in its brittle to ductile transition, it is more difficult to design for crack arrest than to prevent crack initiation (cleavage). This report shows that this is not always true for weldments. Comparison is made between compact crack arrest (CCA), K_a, and crack tip opening displacement (CTOD), K_Jc, toughness for the same HY80 weld. The value of K_a is shown to be much higher than the minimum K_Jc for pop-in fracture initiation. It is considered that the results support the conclusion of Japanese research workers (Arimochi and Isaka) that small pop-ins (in the CTOD test) propagate and arrest without load drop. It follows that prediction of structural failure for weldments need not be based on minimum pop-in toughness from CTOD tests.     

Toughness of glass fibres reinforced glass-ionomer cements

Two fracture toughness parameters, the critical stress intensity factor, K _c and the work of fracture, W _f have been used to characterise the toughness of conventional and resin-modified glass-ionomer cements reinforced with glass fibres. The critical stress intensity factor was determined from the peak load, and the work of fracture was determined as the energy required to extend an introduced crack through the respective glass ionomers. For both materials, crack propagation became more stable as the weight fraction of glass fibres was increased. Additionally, when the weight percent of glass fibres was increased the work of fracture increased. Fibre bridging at the crack tip resulted in the increase in the work of fracture. As the percentage weight of fibres was increased, the critical stress intensity factor decreased proportionally to the increase in porosity.