26Due to uniform shrinkage along the radial direction, drying from both top and bottom surfaces has been 27 recommended to replace drying from outer circumference surface in the restrained circular ring test to assess 28 cracking tendency of concrete. However, non-uniform shrinkage along the height direction under drying 29 conditions is significant, and its effect on crack initiation and propagation in a concrete ring is not clearly 30 understood. To investigate the fracture mechanism of the restrained ring test under drying from top and bottom 31 surfaces, three series of circular and elliptical ring specimens with heights of 30 mm, 50 mm and 75 mm are 32 tested to measure the cracking ages. A fracture mechanics based numerical method is proposed by introducing 33 fictitious crack model to simulate the fracture process and predict the cracking age of a concrete ring under 34 restraint. The effects of ring geometric profile, specimen height and moisture gradient on crack development 35 are discussed. The results indicate that, under drying from both top and bottom surfaces, crack initiates partly 36 along the height direction at the inner circumference of a concrete ring, and propagates along the radial 37 direction, one by one, until the crack propagated throughout the whole cross-section. The moisture gradient 38 along the height direction has significant effect on the crack driving force, which is dominated by the moisture 39 gradient and steel ring restraint near the exposed surface, whose proportion increases with the increase in 40 distance from the exposed surface. 41 42 43 44 45 46 47 1 Introduction 59Concrete is likely to experience shrinkage in response to cement hydration, temperature reduction and 60 moisture dissipation in the process of maintenance, most notably at early ages. When the shrinkage is 61 restrained, cracks initiate easily in concrete structures due to its low cracking resistance, resulting in low 62 structure durability and significant maintenance costs [1]. Therefore, it is important to choose the appropriate 63 laboratory test methods to assess the cracking tendency of concrete used in the field. So far, several test 64 methods have been developed to assess cracking resistance of cementitious materials in the restrained 65 condition, including restrained uniaxial test [2, 3], restrained slab test [4, 5], restrained beam test [6, 7], and 66 restrained ring test [8-12]. Due to its relatively low cost and capacity of providing uniformity end restraint, the 67 restrained ring test has been widely adopted over the other test methods for assessing cracking potential of 68 concrete mixtures. 69 To standardize the restrained ring test, American Association of State Highway and Transportation 70 Officials (AASHTO) (i.e. AASHTO PP34-99: Standard Practice for Cracking Tendency Using a Ring Specimen) 71recommended a certain version of ring specimen: a 75 mm thick concrete ring restrained by a 12.5 mm thick 72 steel ring and dried from its outer circumferential surface. It was reported that, in ...

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In this study the mechanical properties and fatigue behavior of ultra-fine gold wires are investigated by experimental tension fatigue tests and finite element (FE) simulation. Hardening behavior, yield criterion and yield surface of gold wire are determined by tensile tests and force controlled tension fatigue tests. The relationship between plastic strain and loading stress amplitude is determined and the cyclic strain hardening coefficient is calculated. The fatigue data are used to develop a predictive crack model for gold wires bonded in LED packages, based on finite element (FE) stress simulation at temperature cycles (TC). The computer model of the gold wire in the LED package used in the simulation is reconstructed from computer tomography (CT) analysis. The predictive crack model is calibrated using on-line monitoring of LED wire cracks during TC tests. Finally, using the reliability model, the impact of LED package design and material on the wire lifetime is investigated.

The restrained shrinkage elliptical ring test has been established as an efficient method for assessing the cracking potential of concrete at early ages because an elliptical ring can provide a higher degree of restraint compared with a circular one. In this study, a series of circular and elliptical concrete rings restrained by steel rings with various thicknesses were tested under top & bottom surfaces drying or outer circumferential surface drying. By comparing concrete cracking age under different geometrical and drying conditions, the effects of ring geometry, restraining steel ring thickness and drying condition on the cracking process in concrete rings were revealed. Furthermore, numerical analyses were conducted to investigate the fracture mechanism for circular and elliptical rings by applying a fictitious temperature field to simulate the shrinkage effect of concrete. It is found that the increase of steel ring thickness can enhance the degree of restraint, therefore shorten the cracking age for both circular and elliptical rings. However, the improvement is more significant for circular rings. The fracture processes under the two drying conditions, i.e. top & bottom surfaces drying and outer circumferential surface drying are completely different: for drying from outer circumferential surface, the crack initiates at the outer surface and propagates towards the inner surface; for drying from top & bottom surfaces, the crack initiates partially along the height direction at the inner circumference of a concrete ring, and propagates along the radial direction, step by step, until the crack propagates throughout the whole ring wall. In both cases, the self-restraint caused by the non-uniform shrinkage of concrete and the external restraint from the inner steel ring contribute the driving effects for crack propagation. In general, compared with circular rings, the elliptical rings demonstrate the advantage of providing a higher degree of restraint. The elliptical ring test method can, therefore, supplement the traditional circular ring test method for assessing cracking tendency of concrete with higher cracking resistance.

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A new fracture test method was proposed in this study to determine the double-K fracture parameters of concrete, named as the bottom-notched splitting (BNS) test. In the BNS test, the concrete cube with a pre-set crack on the bottom surface was subjected to a line compressive load on the top surface.Numerical analyses were first carried out to simulate the stress distributions along the ligament and crack opening profiles of the BNS specimens. Then, the fitting expressions of the stress intensity factor and the crack center opening displacement were derived based on the linear elastic fracture mechanics.A series of BNS tests and three-point bending (TPB) tests with different ratios of the pre-set crack length to the specimen height were conducted to determine the double-K fracture parameters of the concrete. The results indicated that the pre-set cracks in the BNS tests could initiate and propagate throughout the whole cross-sections of the concrete cubes. By substituting the obtained initial fracture loads, maximum loads and critical crack center opening displacements in the BNS tests into the fitting expressions, the double-K fracture parameters could be determined. By comparing with the TPB tests, the BNS tests were proved to be an effective method to determine the double-K fracture parameters of concrete. The BNS tests were convenient to operate and could reduce the damage risk of the pre-set cracks. Meanwhile, they would be also appropriate for assessing the fracture properties of existing concrete structures in service because the cubes would be easily obtained from the samples core-drilled from existing concrete structures.