Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

The deformation and fracture of balloons

Inflation of balloons provides a straightforward way of achieving large biaxial deformations. Previous studies have shown that when a balloon bursts, crack propagation occurs at very high speed – much higher than would be expected from the low strain modulus and elastic wave velocity of the rubber. The present paper is concerned with studies of the deformation and fracture of cylindrical balloons. On inflation, the deformations of such a balloon pass through an unstable region but subsequently increase monotonically with pressure. In this relatively high pressure region, the ratio of the longitudinal and circumferential extension ratios is broadly in accord with expectations from high-strain elasticity theory when the ratio of the corresponding stresses is taken into account. On bursting, crack speeds up to around 300 m/s in this region. It is shown that these speeds are in accord with large increase in incremental moduli for the highly-strained rubber. Marked changes in crack tip profile observed at very high crack speeds are consistent with control of the rate of growth by inertia rather than by the viscoelastic properties of the rubber (as is believed to be the case at lower speeds). Consistent with this, various elastomers having different glass transition temperatures show similar crack growth behaviour in the very high speed region.     

Tensile properties of microtubules: A study by nonlinear molecular structural mechanics modelling

A nonlinear molecular structural mechanics (MSM) model is proposed in this paper for studying the tensile properties of microtubules (MTs). In the nonlinear MSM models, the interactions between tubulin monomers in MTs are treated as nonlinear axial and torsional springs, whose stiffness coefficients are extracted from all-atom molecular dynamics simulations. The Young's modulus and fracture properties of MTs under tension extracted from the present nonlinear MSM models are found to agree well with the existing simulation and experiment results, which shows the efficiency and accuracy of the proposed nonlinear MSM models. In addition, the nonlinear MSM models are also extended to investigate the tensile properties including Young's modulus and fracture strain of MTs possessing lattice defects. The results obtained from nonlinear MSM models are utilized to develop a predictive equation for quickly predicting the tensile properties of MTs with different lattice defect levels.     

嵌段共聚物相容剂对聚合物共混体系力学性能影响的连续介观模拟

结合介观动力学方法和三维弹簧格子模型, 研究了嵌段共聚物相容剂对相容性较差的聚合物二元共混体系力学性能的影响. 在适当范围内不断增加嵌段共聚物相容剂的用量, 研究了相容剂含量对体系杨氏模数及拉伸强度的影响, 同时也对不同体系材料的破碎位点进行了分析. 结果表明, 未加入相容剂的二元共混体系在拉伸模拟中表现出较低的拉伸强度, 而适量添加相容剂可以显著提升材料的拉伸强度, 随着相容剂含量的增加, 共混体系的破碎位点会发生转移并最终改善材料的整体性能. 而相容剂的加入对体系杨氏模数的影响较小. 该连续模拟方法为关联聚合物复合体系的微观结构和宏观力学性能提供了一条高效的途径.     

Infrared thermographic evaluation of large composite grid parts subjected to axial loading

Many composite parts, such as laminated panels and grid-like shells, operate under high mechanical loading. Evaluation of their structural integrity is crucial to ensure the long-lasting operation of critical components. Since testing a structure under full or “proof” load might be dangerous for personnel, it would be preferable to use a remote, rapid inspection technique. This paper describes a practical application of IR thermography to the inspection of large composite parts used in the aerospace industry. This work has used just one cycle of increasing load from zero load to failure, and this was done for both for tensile and compressive loads. It is shown that, during the formation of micro-defects in polymeric composites, about 40 % of the total dissipated energy is expended for material heating, while about 60 % is related to material damage accompanied by an increase in the defect concentration. Non-uniform composite deformation causes temperature anomalies, whose amplitude may reach 1.5–2.5 °C at a load of about 50–60 % of the limit load.     

Fracture toughness assessment of polypropylene random copolymer with multiple stress modes using the essential work of fracture theory

In recent years, the essential work of fracture (EWF) method has been extensively employed for assessing a material's toughness by specific essential fracture work, especially for polymers showing ductile failure. However, most research has studied either the in-plane stress mode or the out-of-plane stress mode. To obtain a more in-depth understanding of the EWF theory, the specific essential and non-essential fracture work of polypropylene random copolymer (PP-R) was investigated in both in-plane stress mode and out-of-plane stress mode. The effects of ligament length, amount of pre-cracking and pre-cracking method on the specific essential and non-essential fracture work were explored. The specific essential fracture work obtained in both stress modes is compared and discussed.     

Evaluation of hybrid laser-cut and cast miniature fracture specimens

This paper presents a new hybrid laser-cutting method for producing fracture test specimens from thermosetting materials. The hybrid approach combines casting of a sheet of material with subsequent laser-cutting of the test specimens. The new approach was compared to the traditional casting method using a fracture toughness test. For this study, a compact version of the tapered double cantilever beam (cTDCB) was used as a specimen geometry for both manufacturing methods. The cTDCB specimen is crack length independent, and crack length investigations were performed to ensure the crack length independence of the cTDCB specimens. The specimens that were made by the hybrid laser-cut method were found to be comparable to the specimens obtained by the traditional casting method. Moreover, the laser-cut method provides a fast and accurate method to make a significant number of samples in a reasonable time. These tests show that the hybrid laser-cut method could be a good alternative to the traditional casting method.     

Hot tensile fracture characteristics and constitutive modelling of polyether-ether-ketone (PEEK)

The effects of strain rate and deformation temperature on the deformation behaviors of polyether-ether-ketone (PEEK) were studied by uniaxial tensile tests with the temperature range of 23–150 °C and strain rate of 0.01–1 s⁻¹. The effects of deformation temperature and strain rate on the hot tensile deformation behavior and fracture characteristics were investigated by scanning electron microscope (SEM) and discussed in detail. SEM experimental results suggest that fracture morphology is not strain rate sensitive but temperature sensitive. Based on the tensile results, the Johnson-Cook and modified Johnson-Cook constitutive models were established for PEEK. Furthermore, a comparative study has been made on the accuracy and effectiveness of the developed models to predict the flow stress. The results show that the original Johnson-Cook model reflects the deformation behavior more accurately throughout the entire test temperature and strain rate range under uniaxial tensile conditions.     

岩体力学中流变与断裂的耦合作用

本文首先分析含Ｉ型裂纹岩石的流变断裂特性，提出了Ⅰ型裂纹流变断裂初度的三个阈值；然后应用断裂力学和粘塑性理论。得出了具有屈服、蠕变和Ⅱ型裂纹扩展等物理力学特性的岩体隧洞的衬砌与围岩应力的解析表达式。     

Ultrasonic sizing of embedded vertical cracks in ferritic steel welds

Embedded vertical cracks are very often encountered in structural components necessitating reliable procedure for determining their size. Specialized ultrasonic techniques are required for estimation of through thickness height of these cracks [Mater. Eval. (1970) 28; J. NDI 26 (1977) 320; NND (1975) 146]. The conventional pulse-echo technique has serious limitations for quantitative estimation of vertical cracks because it is subject to variations due to reflectivity, coupling factors etc. The present study aims to improve the accuracy of embedded crack height measurement based on transit time rather than the reflected amplitude [NDT Int. (1982) 315; J. JSNDT 27 (1978) 118]. A unique method has been developed for generating known sizes of fatigue cracks ranging from 2.5 to 18 mm in height and 15 mm in length. These cracks were generated in rectangular steel specimens and subsequently embedded at predetermined locations using welding. These welded specimens containing the embedded vertical cracks were examined using ultrasonic techniques based on transit time like (a) flaw tip echo method and (b) mode conversion method. Using both the techniques excellent agreement was obtained between the estimated crack height and actual crack height with an accuracy of ±1 mm.