Strength prediction and failure modes of concrete specimens subjected to the split test

This paper deals with modelling and test of concrete specimens subjected to the Brazilian split test. Based on the fictitious crack concept, a simple model for the crack propagation process in the splitting plane is developed. From the model, it is possible to determine the distribution of residual tensile strength as crack propagation take place. The residual tensile strength is thereafter used in a rigid plastic analysis of the splitting failure. Based on this combined approach, the ultimate load may either be governed by crack propagation or by a plastic failure, which then terminates the crack growth process. It is shown that the model is able to replicate a number of experimental observations. This includes size effect and influence of loading width.     

The Effect of Size on the Splitting Strength of Cubic Concrete Members

In the study of concrete fractures, split‐tension specimens, such as cylinders, cubes and diagonal cubes, are frequently preferred to beams. However, experimental investigations on concrete reveal that for the same specimen geometry, the nominal strength of specimen decreases with increasing specimen size. This phenomenon is named as the size effect in the fracture mechanics of concrete. Although nominal strength is also highly affected by the width of the distributed load in the split‐tension cylinder and cube specimens, this effect can be negligible within the practical range of the load‐distributed width in the diagonal cubes. However, the number of theoretical and experimental studies with diagonal split‐tension specimens is limited. Besides, a size effect formula for estimating the split‐tensile strength of the diagonal cube specimens has not been proposed. In this study, nine series of cube and diagonal cube specimens, with three different sizes but similar geometries, were tested under different load‐distributed widths. The ultimate loads obtained from the test results are analysed by the modified size effect law. Subsequently, prediction formulas are proposed, and they are compared with historical test data from the split‐cylinder specimens.     

循环荷载作用下超高性能混凝土的轴拉力学性能及本构关系模型

对具有不同拉伸应变特性(应变强化和应变软化)的超高性能混凝土(Ultra high performance concrete, UHPC)进行了单调和循环荷载作用下的直接拉伸试验。试验结果表明:应变强化UHPC基体开裂后进入多点微裂纹分布的应变强化段,达到极限抗拉强度后进入单缝开裂的应变软化段;应变软化UHPC基体开裂后直接进入单缝开裂的应变软化段;循环荷载下两种类型UHPC的轴拉应力-应变曲线包络线与单调荷载下的应力-应变曲线基本一致;基于刚度退化过程建立了两种类型UHPC的轴拉损伤演化方程,根据实测应力-应变曲线和试件的裂缝分布形态建立了两种类型UHPC的轴拉本构关系模型,与试验结果基本吻合;采用能量法研究了应变强化UHPC两阶段轴拉本构关系在数值计算时的等效方法。最后,通过无筋应变强化UHPC抗弯试验梁的数值模拟对本文建立的应变强化UHPC轴拉本构关系模型和损伤演化方程及相关假定进行了验证,结果表明本文建立的应变强化UHPC轴拉本构模型能较好地预测UHPC弯拉构件的极限承载力,轴拉损伤变量能在宏观层面上较好地反应试件的裂缝分布状态。      

Softening and snap-back instability in cohesive solids

The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged. For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (K_I = K_IC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.     

Investigation of crack propagation scatter in a gear tooth’s root

This paper describes the problem of determining crack initiation location and its influence on crack propagation in a gear tooth’s root. Three different load positions on the gear tooth’s flank were considered for this investigation of crack initiation and propagation. A special test device was used for the single tooth test. It can be concluded from the measurements that a crack can be initiated at very different locations in a tooth’s root and then propagate along its own paths. A numerical investigation into a crack initiation’s position and its influences on its propagation were carried out within the framework of linear fracture mechanics. The influence of a tooth’s load position, the geometry of the tooth’s root, and the influence of non-parallel load distribution on the tooth’s flank were considered when investigating the crack initiation’s position. Results show that linear fracture mechanics can be used for determining crack propagation, if better initial conditions for crack initiation are considered.     

Mixed mode fracture energy of sprucewood

The characterization of Mixed Mode (Mode I and Mode II) behaviour of wood was concentrated on concepts of linear fracture mechanics in the past. Using an adopted version of the splitting test it was possible to obtain complete load displacement curves under different Mixed Mode loading cases for crack propagation along the grain. Therefore fracture energy concepts (specific fracture energy) could be used to characterize the material behaviour. Additionally strength parameters were used in order to describe crack initation in two crack propagation systems. The values for specific fracture energies as well as the strength values were compared with pure Mode I fracture tests. Moreover, the size effect under Mixed Mode loading was investigated to guarantee size independent material characterizing values for the specific fracture energies.     

Thin layer splitting along the elastic-plastic solid surface

Thin layer splitting along the elastic-plastic solid surface is studied based on the elastic-plastic fracture mechanics method. In the splitting process, since the split arm does not undergo the reversed plastic bending, comparing with the conventional peel test method, the split test has remarkable advantages in measuring the material fracture behavior and is recommended as a new test method. Moreover, besides the driving force parameter, the split test method provides an additional measurable parameter, a residual curvature (or curvature radius) of the split arm. Comparing with the peeling force, the split force also has the connection with the total energy release rate, which is related with the crack tip separation energy (or material fracture toughness), separation strength, and the plastic dissipation work. Through measuring the driving force and the residual curvature, the fracture toughness and separation strength can be obtained. The primary objective of the present research is to develop a series of relations of the split force, the residual curvature, as well as the crack tip slope angle, respectively with the split layer thickness and material parameters, when crack tip advances steadily. Frictionless (or smooth) contact between splitter head and split arm surface is assumed. Another objective of the present research is to explore a connection between the split test solutions and the peel test solutions. Finally, the split test analysis is applied to a wedge-loaded double-cantilever beam experiment for Al-alloy material, a considerably similar test method with the split test, conducted by Thouless and his collaborators, and the fracture parameters from both test systems are correlated.     

Influence of short-fibre reinforcement on the mechanical and fracture behaviour of polycarbonate/Acylonitrile Butadiene Styrene polymer blend

The present study investigated the dependence of various mechanical and fracture properties on the volume fraction, f, of the reinforcing glass fibres in Polycarbonate/Acylonitrile Butadiene Styrene (ABS) blends. The addition of glass fibres enhanced the ultimate tensile strength and modulus and reduced elongation (both to yield and to break) and total work of fracture. The elastic modulus was not significantly affected by the loading mode although the ultimate strength was significantly affected, giving flexural strength values of 1.5–1.6 times greater than tensile strengths. The elastic modulus and strength were linear functions of f and thus followed the principle of rule of mixtures. The presence of weldlines in specimens had an adverse effect on most tensile properties except for the elastic modulus. Linear elastic fracture mechanics could not be used to assess the resistance to crack propagation of the present range of materials because their behaviour violated the principle assumptions upon which the theory is based. An alternative method was employed where the total work of fracture and the work of fracture corresponding to the maximum load were plotted as a function of initial crack length. These plots were reasonably linear for the polymer and its composites giving values of the resistance to steady state crack propagation JT and the J integral of maximum load Jm respectively. Values of JT and Jm decreased with increasing f.     

Constitutive relations for split cylinder tests on bituminous concrete

The scope of this progress report was to a determine the constitutive relations for asphaltic concrete using the split cylinder test for two percents of bitumen, and b. compare the results with uniaxial tensile data on asphaltic concrete to assess the suitability of the split cylinder test for routine material characterizations. A special digital computer routine was used to reduce the experimental data, develop the constitutive relations, and perform the statistical analysis. Using the procedures reported here, the split cylinder tests, compared with uniaxial tension tests, overestimated the strain at high rates of loading, underestimated at very low rates of loading, and the ultimate strain values for the two test methods were the same for a value of R of about 0.1%/min. The split cylinder test underestimated the ultimate tensile stress by about one-half an order of magnitude for all values of strain rate that would be used in highway work.     

Microstructure and fracture behavior of non eutectic Sn–Bi solder alloys

The microstructure and mechanical properties of Sn–xBi (x = 10, 20, 25, and 35) solder alloy were investigated by scanning electronic microscope and notch tensile test. The results showed that the microstructure of Sn–10Bi and Sn–20Bi solder alloy was constituted by Bi particle and β-Sn phase. The microstructure of Sn–25Bi and Sn–35Bi solder alloy was consisted of eutectic phase and primary phase. The ultimate tensile load of Sn–20Bi solder alloy was higher than that of Sn–10Bi in notch tensile test. The ultimate tensile load of Sn–25Bi and Sn–35Bi was declined gradually compared with that of Sn–20Bi solder alloy. The fracture energy of Sn–xBi was decreased continuously when the Bi fraction increased. Crack observation, fracture surface observation, and finite element analysis revealed that the crack initiation and propagation of Sn–25Bi and Sn–35Bi was dominated by the fracture of brittle eutectic phase. Therefore, the ultimate tensile load and fracture energy of Sn–25Bi and Sn–35Bi were damaged compared with that of Sn–20Bi.     

Influence of defects on fatigue crack propagation in laser hybrid welded eccentric fillet joint

Fatigue cracking of laser hybrid welded eccentric fillet joints has been studied for stainless steel. Two-dimensional linear elastic fracture mechanics analysis was carried out for this joint geometry for four point bending load. The numerical simulations explain for the experimental observations why the crack propagates from the lower weld toe and why the crack gradually bends towards the root. Lack of fusion turned out to be uncritical for the initiation of cracks due to its compressive stress conditions. The linear elastic fracture mechanics analysis has demonstrated in good qualitative agreement with fatigue test results that lack of fusion slightly (<10%) reduces the fatigue life by accelerating the crack propagation. For the geometrical conditions studied here improved understanding of the crack propagation was obtained and in turn illustrated. The elaborated design curves turned out to be above the standard recommendations.     

Stable crack growth in a surface compression-strengthened hollow cylinder

In this paper the static fatigue problem for a circumferentially cracked hollow cylinder is examined. For this particular configuration, stable crack growth, in the absense of any external forces, is determined for cylinders with axial components of residual stress which are compressive on the inner and outer radial surfaces and tensile in the cylinder wall. An initial surface crack which is deep enough to penetrate the compression strengthened surface region and enters the tensile zone may propagate in a stable manner until either sudden spontaneous failure occurs or the crack arrests. Since a portion of the crack near the cylinder surface will be closed because of the compressive residual stress field, an additional unknown in the problem is the extent of the crack surface contact. This crack surface contact length is determined by iteration on the integral equation which arises in the mathematical derivation for an embedded circumferential crack in a hollow cylinder. As an illustration of stable crack growth for this geometry with a realistic residual stress distribution, numerical results are presented for a hollow, soda-lime glass cylinder, based on crack growth rates in soda-lime glass exposed to water at 25‡ C. Using the fracture toughness and slow crack growth characteristics for soda-lime glass, the conditions for no crack propagation, crack propagation leading to crack arrest, and catastrophic failure are established.     

AN EXPERIMENTAL INVESTIGATION INTO THE OPERATIONAL SAFETY OF A WELDED PENSTOCK BY A FRACTURE MECHANICS APPROACH

Abstract—Three different fracture mechanics approaches were applied to two full-scale penstock model tests. The two models were produced, using a Sumiten 80P HSLA steel (minimum yield strength 700 MPa and minimum ultimate tensile strength 800 MPa), in the form of pressure vessels. The first experiment was a burst test performed on a pre-cracked model to determine crack arrest properties. The second experiment was a hydro-pressure test on a model with no cracks and this enabled a post-yield experimental analysis of the undermatched weld metal, when cracks did not initiate. Crack driving forces, obtained numerically, and J-R curves, obtained by the J -integral direct measurement on tensile panels, were used to predict the residual strength. The overall behaviour of a welded penstock under load was analysed on the basis of the results of these three approaches, allowing an evaluation of the significance of cracks.     

Simulation of crack propagation of fiber reinforced cementitious composite under direct tension

Mode I crack propagation in fiber reinforced cementitious composite is simulated based on fracture mechanics criteria. To analyze crack propagation, a superposition method is employed to calculate the stress intensity factor at the crack tip resulted from both the applied load and the crack bridging stress. Using the model, the effects of various material parameters on the tensile performance are investigated. The requirements for tensile strain-hardening and multiple cracking are analyzed and possible methods for material performance optimization are discussed. Finally, predicted behavior is verified by tensile and bending tests performed on two fiber reinforced cementitious composite beams.     

Dimensional analysis for concrete in fracture

A structural element of high strength in compression and extremely low strength in tension, such as concrete, is considered. Based on linear-elastic fracture mechanics a simple model law for ultimate load was derived by the author in 1986. This model law is shown also to be consistent with the non-linear fracture mechanical theory called the fictious crack model.     

Size effect and boundary conditions in the brazilian test: theoretical analysis

Splitting strength determined in the Brazilian test is assumed to be a property independent of size and uniquely related to the intrinsic material strength. However, as was experimentally demonstrated by various authors, the splitting strength depends on the specimen size. In this paper, the size effect in the Brazilian test is analyzed theoretically using a nonlinear fracture model based on cohesive crack concepts and the results obtained are compared with the classical strength limit approach. Two important variables are studied: the load-bearing strip and the geometry of the specimen. From the numerical results a closed form expression is proposed, dependent on the width of the bearing strip and on geometry. The results confirm that splitting strength decreases with the specimen size, tending towards an asymptotic solution for large size specimens. Within the size range analyzed (0.1 m to 2.5 m diameter for typical concrete) the splitting strength can vary by up to 25% in cylindrical specimens and by up to 35% in prismatic square section specimens, although this size effect is strongly dependent on the load-bearing strip. For widths of bearing strip smaller than 4% of the specimen diameter, the effect of the specimen size is negligible and the splitting strength approaches the tensile strength for any practical specimen size.     

均匀化处理对Mg-13Gd-3.5Y-2Zn-0.5Zr镁合金组织和力学性能的影响

对Mg-13Gd-3.5Y-2Zn-0.5Zr镁合金铸锭进行均匀化处理,温度为505～525℃,时间为4～24h,并采用光学显微镜(OM)、扫描电子显微镜(SEM)、X射线衍射仪(XRD)和万能材料试验机等检测手段分析均匀化处理前后合金微观组织和力学性能的变化。结果表明:均匀化处理后,原始组织中网状分布共晶化合物转化成晶界处不连续分布的块状LPSO相,离散分布的方块状富稀土相溶解。力学性能测试显示,铸态镁合金的抗拉强度为172.9MPa,伸长率为1.8%,经过均匀化处理后合金的力学性能得到提高,在515℃/16h均匀化制度下,合金室温抗拉强度为212.3MPa,伸长率为3.1%;在200℃下抗拉强度为237.2MPa,伸长率为9.7%,性能达到最佳。断口扫描显示,铸态合金是以撕裂棱与解理台阶为主的解理脆性断裂,均匀化处理后的合金中出现小而浅的韧窝,但仍然是以解理台阶为主的准解理断裂,塑性提高有限,长程有序相可成为裂纹的萌生源。     

Effect of bolt clamping force on the fracture strength of mixed mode fracture in an edge crack with different sizes: Experimental and numerical investigations

To investigate the effect of bolt clamping force, resulting from torque tightening, on the mixed mode fracture (I and II) strength and effective geometry/loading factor of an edge crack with different lengths, experimental and numerical studies have been carried out. In the experimental part fracture tests were conducted on three batches of simple edge crack and bolt torque tightened with 3.5 and 7 N m edge crack at three different crack sizes of Poly methyl-methacrylate (PMMA) rectangular plate. The specimens’ fracture strength was obtained using a tensile test machine at different loading angles by employing a modified Arcan fixture. In numerical part, finite element simulations were employed to model the three test specimen batches at the three crack lengths to obtain their stress intensity geometry/loading factors. The results show that the bolt tightening torque significantly reduces the effective geometry/loading factor, and thus increases the joint fracture strength compared to bolt-less simple edge crack specimens. However, the bolt clamping effect on increasing the fracture strength was almost the same for different crack lengths.     

Analysis of mixed-mode fracture in concrete using interface elements and a cohesive crack model

The paper presents a model, based on nonlinear fracture mechanics, for analysing crack propagation in quasi-brittle materials, such as concrete. The work is limited to two-dimensions, and therefore, the fracture modes of interest are mode I (pure tension) and mode II (pure shear). The constitutive model has been implemented in the context of the finite element method using interface elements. The fracture is simulated through a discrete crack represented by the interface with a cohesive crack stress-separation relation derived from the model, which is based on a fracture criterion, together with a flow rule and a softening law. The model is used for simulating results from an experimental study on beams with centric and eccentric notches of high and normal strength concretes, and explaining other test results available in the literature.     

On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture

In this paper, strong discontinuities embedded in finite elements are used to model discrete cracking in quasi-brittle materials. Special attention is paid to (i) the constitutive models used to describe the localized behaviour of the discontinuities, (ii) the enforcement of the continuity of the crack path and (iii) mixed-mode crack propagation. Different constitutive relations are adopted to describe the localized behaviour of the discontinuities, namely two damage laws and one plasticity law. A numerical algorithm is introduced to enforce the continuity of the crack path. In the examples studied, an objective dissipation of energy with respect to the mesh is found. Examples of mode-I and mixed-mode crack propagation are presented, namely a double notch tensile test and a single-edge notched beam subjected to shear. In the former case different crack patterns are obtained depending on the notch offset; in the latter case special emphasis is given to the effect of shear on the global structural response. In particular, both the peak load and the softening response of the structure are related to the amount of shear tractions allowed to develop between crack faces. The results obtained are compared to experimental results. As a general conclusion, it is found that crack path continuity allows for the development of crack patterns similar to those found in experiments, even when reasonably coarse meshes are used.