Size-Effect Testing of Cohesive Fracture Parameters and Nonuniqueness of Work-of-Fracture Method

The cohesive crack model has been widely accepted as the best compromise for the analysis of fracture of concrete and other quasibrittle materials. The softening stress-separation law of this model is now believed to be best described as a bilinear curve characterized by four parameters: the initial and total fracture energies Gf and GF, the tensile strength ft′, and the knee-point ordinate σ1. The classical work-of-fracture test of a notched beam of one size can deliver a clear result only for GF. Here it is shown computationally that the same complete load-deflection curve can be closely approximated with stress-separation curves in which the ft′ values differ by 77% and Gf values by 68%. It follows that the work-of-fracture test alone cannot provide an unambiguous basis for quasibrittle fracture analysis. It is found, however, that if this test is supplemented by size-effect testing, all four cohesive crack model parameters can be precisely identified and the fracture analysis of structures becomes unambiguous. It is shown computationally that size-effect tests do not suffice for determining GF and ft′, which indicates that they provide a sufficient basis for computing neither the postpeak softening of fracturing structures nor the peak loads of a very large structure. However, if the size-effect tests are supplemented by one complete softening load-deflection curve of a notched specimen, an unambiguous calculation of peak loads and postpeak response of structures becomes possible. To this end, the notched specimen tests must be conducted in a certain size range, whose optimum is here established by extending a previous analysis. Combination of the work-of-fracture and size-effect testing could be avoided only if the ratios GF/Gf and σ1/ft′ were known a priori, but unfortunately their estimates are far too uncertain.     

Direct Tensile Tests on Concretelike Materials: Structural and Constitutive Behaviors

The complete stress-strain and stress-crack opening response of a concretelike material loaded in tension is examined starting from a series of displacement-controlled tests on notched cylinders, whose end sections were prevented from rotating (fixed platens). The test results refer to two very high-strength cementitious composites (tensile strength fc ≈ 160–165 MPa) and one “reference” high-strength concrete (fc ≈ 90 MPa). Their behavior (pseudoelastic up to first cracking and cohesive after crack localization) is analyzed to identify the nonlinear stress-strain and stress-crack opening response and to distinguish it from the structural behavior of the specimens. The ascending branch is modeled by studying the stresses at the notch tip by means of Neuber's approach based on stress concentration factors. As for concrete softening (falling branch), an appropriate cohesive law is introduced. Finally, the structural response associated with progressive cracking is systematically analyzed, and once more, it is shown that the load-displacement relationship obtained in a test is hardly a material property.     

Use of Material Interfaces in DEM to Simulate Soil Fracture Propagation in Mode I Cracking

Mode I fracture is common in geomechanics in desiccation cracking, hydraulic fracture, and pressuremeter testing. The cohesive crack model has been used extensively and successfully in numerical modeling of such fracture in concrete and steel but has not been applied in modeling of soil fracture to the same extent. It is argued that the cohesive crack model may be more appropriate than linear elastic fracture mechanics (LEFM) for soils because it takes into account finite tensile strength and any likely plasticity during fracture. With special reference to the Universal Distinct Element Code (UDEC) computer program, a methodology of using interfaces in the distinct element method (DEM) of analysis to model fracture has been validated herein, and this approach is considered to be useful in geomechanical modeling applications. The methodology is based on the cohesive crack approach and shows how softening laws could be back-calculated from load-displacement curves of test specimens. It has been validated using three geometries: a tension test with a rectangular cross section, a notched three-point bend beam, and a compact tension test. Approximate softening laws for St. Albans clay from Canada are proposed.     

Fictitious Crack Propagation in Fiber-Reinforced Concrete Beams

A nonlinear cracked hinge model is developed, aimed at the analysis of the bending fracture of fiber-reinforced concrete beams. The model is based on the fracture mechanics concepts of the fictitious crack model with a bilinear stress-crack opening relationship. Closed-form solutions are presented for the moment-rotation relationship of the hinge as a crack propagates, and the case of a nonzero normal force is covered. Special shapes of the stress-crack opening relationship are treated separately. These shapes are the so-called drop-linear and the drop-horizontal for which simplified expressions are obtained. The applicability of the hinge model is demonstrated through analysis of the bending fracture process in the case of a three-point bending beam and an infinitely long beam on a Winkler foundation, the latter analysis comprising the effect of a constant tensile normal force.     

Hydrogen-assisted ductile fracture in spheroidized 1520 steel: Part II. Pure bending

The effects of hydrogen on ductile fracture were investigated in a spheroidized steel similar to AISI 1520, containing negligible amounts of P and S, using notched bend bar tests. The effects of hydrogen were exhibited either in the form of enhanced plastic instability along characteristic slip traces in mode II or of enhanced, strain-controlled, local crack tip processes. The contri-bution of enhanced plastic instability, however, was only apparent under conditions in which flow localization also occurred without hydrogen. The role of plastic instability near the crack tip was found to be dominant in these bend bar tests, whereas it was small or negligible in previous tests in axisymmetric tension. Microstructural effects were rationalized in terms of a critical, local concentration of hydrogen. The intrinsic effect of hydrogen appeared to be the enhancement of strain-controlled fracture processes. Formerly with Carnegie Mellon University.     

Cleavage fracture of steels at low temperatures

Model of cleavage fracture: deformation twin creates microcrack in cementite lamella; critical event in fracture process is extension of crack into ferrite under the action of twin and applied stresses. Stress analysis of the model yields fracture stress. Mechnical tests with tension, compression and notched bend specimens at temperatures 4 K < T < 100 K. Evaluation of local fracture stress by finite element analysis. Comparison of theoretical and experimental results.     

Analysis of Crack Tip Stress of Transversal Crack on Slab Corner During Vertical-Horizontal Rolling Process by FEM

Behavior of transversal crack notched on slab corner during vertical-horizontal rolling process was simulated by FEM. The crack tip stress in the whole rolling process was obtained. Influences of the friction coefficient, the initial crack size, the edger roll profile, and the groove fillet radii of grooved edger roll on crack tip stress were analyzed. For vertical rolling, the tension stress appears at crack tip near the slab top surface and the compression stress appears at crack tip near the slab side surface for the flat edger roll; however, the compression stress appears at crack tip near the slab top surface and the tension stress appears at crack tip near the slab side surface in the exit stage for the grooved edger roll. For horizontal rolling, the tension stress appears at crack tip just at the exit stage for the flat edger roll, and the tension stress appears in whole rolling stage; the tension stress value near the slab side surface is much larger than that near the slab top surface for the grooved edger roll.     

Simulation of Crack Propagation in Asphalt Concrete Using an Intrinsic Cohesive Zone Model

This is a practical paper which consists of investigating fracture behavior in asphalt concrete using an intrinsic cohesive zone model (CZM). The separation and traction response along the cohesive zone ahead of a crack tip is governed by an exponential cohesive law specifically tailored to describe cracking in asphalt pavement materials by means of softening associated with the cohesive law. Finite-element implementation of the CZM is accomplished by means of a user subroutine using the user element capability of the ABAQUS software, which is verified by simulation of the double cantilever beam test and by comparison to closed-form solutions. The cohesive parameters of finite material strength and cohesive fracture energy are calibrated in conjunction with the single-edge notched beam [SE(B)] test. The CZM is then extended to simulate mixed-mode crack propagation in the SE(B) test. Cohesive elements are inserted over an area to allow cracks to propagate in any direction. It is shown that the simulated crack trajectory compares favorably with that of experimental results.     

Damage-mechanics-based modelling of failure of squeeze-cast AM50 magnesium alloy

Static and impact tests on bars and plates of squeeze-cast AM50 were used to calibrate a failure surface that depends on tri-axiality and Lode angle. Both notched and un-notched bars and plates were tested. Assuming isotropic plastic response, but asymmetry of work hardening in compression and tension, a damage-mechanics-based model is used to model static and impact loading. Predictions using the model are found to be in reasonable agreement with the experimental results; peak loads and ductility are well described by the model, particularly, for engineering applications. Qualitatively, the model predicts the crack growth in good agreement with observations for experiments wherein the tri-axiality is higher. Likewise, the predicted deformation and failure response are in good agreement with the experimental deformation and failure for higher tri-axiality experiments. We suggest that owing to the coarse grain size, at high levels of deformation, the response is not uniform which make continuum-based modelling a challenge. Nevertheless, the present effort is suitable for predictions of failure in engineering practice.     

Fracture Behavior of Acrylonitrile Butadiene Styrene (ABS) Hybrid Composites Reinforced with Nano Zirconia and Poly Tetra Fluoro Ethylene (PTFE)

ABS composites were processed using melt blending technique by twin screw extrusion and further employing compression molding process. Microstructure and characterization analysis were carried out on the ABS composites as well as pure ABS through XRD, TEM and SEM. Mode I fracture toughness behavior were studied by conducting compact tension test. Short beam shear strength of the composites were determined by carrying out short beam strength test. Fractographic analysis was done using SEM in order to study the various toughening mechanisms involved. XRD studies revealed that nano zirconia and PTFE has formed an uniform structure with ABS polymer, which has also been confirmed with microstructural analysis. Addition of nano zirconia up to 1.5% increases the toughness, which can be attributed to crack bowing and crack deflection. With further addition of nano zirconia, fracture toughness get reduced as the composite become brittle in nature which improves strength but reduces the toughness. It has been observed that addition of PTFE enhances fracture toughness which is ascribed to the crack pinning, cavitation, crack bowing and crack deflection. The increase in shear strength can be due to toughening mechanisms which are evident from the presence of shear cusps, crack pinning and extensive plastic deformation.     

Fracture behaviours of fracture toughness testing specimens with metallurgical heterogeneity along crack front

Safe use of welded structures is dependent on fracture mechanics properties of welded joints. In present research, high strength low alloyed HSLA steel in a quenched and tempered condition, corresponding to the grade HT 80, was used. The fluxo cored arc welding process (FCAW), with CO₂ as shielding gas, was used and two different tubular wires were selected. The aim of this paper is to analyse fracture behaviour of undermatched welded joints, and also to determine relevant parameters which contribute to higher critical values of fracture toughness. Towards this end three differently undermatched welded joints were analysed using results of testing the composite notched specimens with through thickness crack front positioned partly in the weld metal, partly in heat affected zone (HAZ) and partly in base material (BM).The presence of different microstructures along the pre‐crack fatigue front has an important effect on the critical crack tip opening displacement (CTOD). This value is the relevant parameter for safe service of welded structure. In the case of specimens with through thickness notch partly in the weld metal, partly in the heat affected zone and partly in the base material, i.e. using the composite notched specimen, fracture behaviour strongly depends on a partition of ductile base material, size and distribution of mismatching factor along vicinity of crack front. If local brittle zones occur in the process zone, ductile base metal can not prevent pop‐in instability, but it can reduce it to an insignificant level while the fracture toughness parameter is higher and the weakest link concept can not be applied.     

锌锅用热轧钢板解理断裂行为分析简

 通过断裂试样断口的宏观和显微分析、显微组织表征、拉伸和冲击试验以及解理断裂应力条件,讨论分析了锌锅用低强度级别钢板弯曲成形断裂的微观解理断裂行为。结果表明,钢板发生解理断裂的微观机制与冲击试样断裂相同,即晶粒尺寸控制的穿过晶界的裂纹扩展是解理断裂的临界事件。粗大的铁素体晶粒的面积分数过高显著降低了裂纹扩展阶段所需的局部解理断裂应力σf。断口宏观分析判断在钢板边部应存在导致应力集中的初始裂纹源,这极大降低了启动解理断裂的断裂应力并同时提高裂纹源前端的正应力σyy,扩大了解理断裂活跃区至初始裂纹前端,从而不可避免地发生脆性解理断裂。     

High-temperature rupture of microstructurally unstable 304 stainless steel under uniaxial and triaxial stress states

Specimens of 304 stainless steel were tested to failure under two different stress states, uniaxial tension using smooth bar specimens and triaxial tension using notched bar specimens. The tests were conducted at a temperature that gives rise to carbide particle growth which, in turn, leads to microstructural softening. Rupture times are compared for uniaxial and triaxial stress states with respect to multiaxial stress parameters that are directly related to physical mechanisms. The success of the parameters is judged according to how well the rupture times of notched specimens can be predicted using the rupture data for specimens under uniaxial tension. The data indicate that the rupture time is not governed by deformation processes, despite evidence for substantial softening by particle coarsening. The results further suggest that the creep rupture process is dominated by cavitation that is coupled with localized shear deformation along the inclined grain boundaries.     

The effect of environment on the sustained load crack growth rates of forged WASPALOY

The sustained load crack growth rates of wrought WASPALOY* were measured in air and in high purity argon at 650 °C using single edge notched (SEN) and compact tension (CT) specimens machined out of a turbine disk. The crack growth rates measured in air exhibited great variability across the WASPALOY disk, while the crack growth rates measured in purified argon were of the same order of magnitude. This difference in crack growth rates is attributed to local variations in oxidation resistance at the tip of the growing crack. The density and the distribution of carbides in different locations of the WASPALOY disk accounts for the variability in crack growth resistance in air.     

Fatigue Fracture of Concrete Subjected to Biaxial Stresses in the Tensile C–T Region

In this paper cyclic quasi-static and constant amplitude fatigue responses of concrete subjected tensile compression–tension (C–T) biaxial stress are presented. In the tensile C–T region within the biaxial stress space, magnitude of the principal tensile stress is larger than or equal to that of the principal compressive stress. An experimental program consisted of subjecting hollow, cylindrical concrete specimens to torsional loading. Failure in both quasi-static and fatigue is due to crack propagation. It is shown that the crack propagation resulting from the biaxial loading can be predicted using Mode I fracture parameters. The fatigue crack growth is observed to be a two-phase process: an acceleration stage that follows a deceleration stage. The crack length where the rate of crack growth changes from deceleration to acceleration is shown to be equal to the crack length at the quasi-static peak load. Analytical expressions for crack growth in the deceleration and acceleration stages are developed in terms of the mechanisms that influence quasi-static crack growth. The model parameters obtained from uniaxial fatigue tests are shown to be sufficient for predicting the biaxial fatigue response. Finally, a fracture-based fatigue-failure criterion is proposed, wherein the fatigue failure can be predicted using the critical Mode I stress intensity factor.     

Fatigue Crack Prognostics by Optical Quantification of Defect Frequency

Defect frequency, a fatigue crack prognostics indicator, is defined as the number of microcracks per second detected using a laser beam that is scanned across a surface at a constant predetermined frequency. In the present article, a mechanistic approach was taken to develop a methodology for deducing crack length and crack growth information from defect frequency data generated from laser scanning measurements made on fatigued surfaces. The method was developed by considering a defect frequency vs fatigue cycle curve that comprised three regions: (i) a crack initiation regime of rising defect frequency, (ii) a plateau region of a relatively constant defect frequency, and (iii) a region of rapid rising defect frequency due to crack growth. Relations between defect frequency and fatigue cycle were developed for each of these three regions and utilized to deduce crack depth information from laser scanning data of 7075-T6 notched specimens. The proposed method was validated using experimental data of crack density and crack length data from the literature for a structural steel. The proposed approach was successful in predicting the length or depth of small fatigue cracks in notched 7075-T6 specimens and in smooth fatigue specimens of a structural steel.     

Detecting Multiple Open Cracks in Elastic Beams by Static Tests

This paper concerns with the identification of multiple open cracks in a beam by measurements of the damage-induced variations in the static deflection of the beam under a prescribed load condition. Each crack is simulated by an equivalent linear spring connecting the two adjacent segments of beam. Sufficient conditions on the static measurements which allow for the unique identification of the damage are presented and discussed for nonuniform beams under some ideal boundary conditions. The inverse analysis is based on an explicit expression of the crack-induced variation in the deflection of the beam under a given load distribution and it provides exact closed-form expressions of position and severity of the cracks in terms of the measured data. The theoretical results are confirmed by a comparison with static tests carried out on a steel beam with localized damages.     

浅谈后张法有粘结预应力梁施工工艺

本文旨在更有效地利用高强钢材,弥补混凝土与钢筋拉应变之间的差距,把预应力运用到钢筋混凝土结构中去。亦即在外荷载作用到构件上之前,预选建立有内应力的混凝土,通过对预应力筋进行张拉、锚固、放松,借助钢筋的弹性回缩,使受拉区混凝土事先获得预压应力。当构件承受由外荷载产生的拉力时,首先抵消混凝土中已有的预压力,然后随荷载增加,才能使混凝土受拉而后出现裂缝,因而延迟了构件裂缝的出现和开展。     

Effects of Size and Slenderness on Ductility of Fracturing Structures

The ductility of an elastic structure with a growing crack may be defined as the ratio of the additional load-point displacement that is caused by the crack at the moment of loss of stability under displacement control to the elastic displacement at no crack at the moment of peak load. The stability loss at displacement control is known to occur when the load-deflection curve of the whole structural system with the loading device (characterized by a spring) reaches a snapback point. Based on the known stress intensity factor as a function of crack length, the well-known method of linear elastic fracture mechanics is used to calculate the load-deflection curve and determine the states of snapback and maximum loads. An example of a notched three-point bend beam with a growing crack is analyzed numerically. The ductility is determined and its dependence of the structure size, slenderness, and stiffness of the loading device is clarified. The family of the curves of ductility versus structure size at various loading device stiffnesses is found to exhibit at a certain critical stiffness a transition from bounded single-valued functions of D to unbounded two-valued functions of D. The method of solution is general and is applicable to cracked structures of any shape. The flexibility (force) method can be adapted to extend the ductility analysis to structural assemblages provided that the stress intensity factor of the cracked structural part considered alone is known. This study leads to an improved understanding of ductility, which should be useful mainly for design against dynamic loads.     

Tripartite Cohesive Crack Model

A new multicomponent cohesive crack model for concrete is presented. The model, which is directly applicable to interface finite elements, has three main components termed undamaged, bridging, and fully debonded. The relative sizes of these components, each of which simulates a proportion of a representative material volume, change according to evolution functions that are developed from data from uniaxial cyclic tests on notched concrete specimens. The undamaged component is treated as elastic damaging, the bridging component has two subcomponents, which are elastoplastic and elastic with contact, and the fully debonded component is elastoplastic with contact. The relationships governing the normal-shear interactions are developed from experimental data on combined shear-tension tests on cracked concrete specimens. Comparisons with experimental data illustrate that the model is able to represent the cyclic behavior of cracked concrete in tension, full crack closure, the interaction between shear and normal behavior, and aggregate interlock behavior.