Tension-softening

Li, V.C., Wang, Y., and Backer, S. (1991) A statistical-micromechanical model of tension-softening behavior of short fiber reinforced brittle matrix composites , Journal of Mechanics and Physics of Solids, Vol. 39, No. 5, 1991, 607-625. 

It is well known in concrete engineering that the fracture process zone is created ahead of a notch (crack) in concrete, without revealing the notch sensitivity. Nucleation of micro-cracks in the fracture process zone is clarified as shown in Fig. 10.25 (Nomura, Mihashi et al. 1991). The fracture process zone was ideally introduced in order to explain the tension-softening behavior. Then, as shown in the figure, the presence of the zone is physically confirmed. 

Nomura N, Mihashi H, Niiseki S (1991) Influence of coarse aggregate size on fracture energy and tension softening of concrete. Concrete Research and Technology JCI 2(l) 57-66... 

The cracking of the concrete can be specified as a combination of tension cut-off, tension softening, and shear retention (Fig. 13.3). The tension cut-off criterion is a linear stress cut-off. The tension softening criterion was set to be nonlinear tension softening with ultimate strain. The shear retention criterion was set to be a constant shear retention factor defined by a constant p value. 

Fig. 13.3 (a) Linear tension cut-off, (b) nonlinear tension softening, (c) constant shear retention factor... 

In the DIANA model, the shear retention factor f) must be assumed. For closed cracks, the coefficient is assumed to be 1.0 smaller f) value resulted in premature failure. Also, a nonlinear tension softening was selected to describe the relation between the tensile stress and tensile strain at the cracked elements. 

Fracture in the process zone before the crack tip in elements under direct tension, or in tensile zones of elements subjected to bending, was represented by different models. In these models, the transfer of stress across the process zone is related to displacement in the crack by a so-called tension-softening diagram. The form of this diagram represents a constitution law, which is characteristic for the considered material. 

Various methods of determination of the tension-softening diagrams, which express the behaviour of different materials at fracture, were proposed for example, the so-called crack band approach was described by Bazant and Planas (1998), and a general review of the state of knowledge by Bazant (2002). The application of the notion of R-curves was again approached by Vesely and Kersner (2006) without conclusive results. 

The problem of secondary flexure in axial tensile tests is considered in view of the tension-softening process. The procedures aimed at elimination of that parasite effect were studied by Akita et al. (2001) and Novak et al. (2006) who have shown possibilities of nonlinear fracture mechanics simulation in analysis of the experimental data, including post-peak descending branch of the load-displacement curves, taking into consideration material imperfections and heterogeneities. 

V.C. Li, Y. Wang and S. Backer, A micromechanical model of tension softening and bridging toughening of short random fiber reinforced brittle matrix composites , J. Mech. Phys. Solids. 39,1991, 607-625. 

D. Lange-Kornbak and B.L. Karihaloo, Tension softening of short-fibre-reinforced cementitious composites , Cem. Concr. Compos. 19,1997,315-319. 

Net-tension failures can be avoided or delayed by increased joint flexibility to spread the load transfer over several lines of bolts. Composite materials are generally more brittle than conventional metals, so loads are not easily redistributed around a stress concentration such as a bolt hole. Simultaneously, shear-lag effects caused by discontinuous fibers lead to difficult design problems around bolt holes. A possible solution is to put a relatively ductile composite material such as S-glass-epoxy in a strip of several times the bolt diameter in line with the bolt rows. This approach is called the softening-strip concept, and was addressed in Section 6.4. 

Another way to obtain a seed is to dip a capillary tube into the melt. Surface tension causes the tube to fill and when it freezes inside, a smcdl seed results. The difficulty with this method is that it is difficult to obtain a tube of proper diameter, made of the proper material. Glass softens at too low a temperature and quartz melts around 1400-1500 °C. Usually, we are restricted to metals and even then, we must be able to cut the tube to obtain the seed, since it is confined within the tube. Once in a while, we can use the tube directly and obtain growth directly upon the seed, even though it has remained within the tube. 

In our approach to membrane breakdown we have only taken preliminary steps. Among the phenomena still to be understood is the combined effect of electrical and mechanical stress. From the undulational point of view it is not clear how mechanical tension, which suppresses the undulations, can enhance the approach to membrane instability. Notice that pore formation models, where the release of mechanical and electrical energy is considered a driving force for the transition, provide a natural explanation for these effects [70]. The linear approach requires some modification to describe such phenomena. One suggestion is that membrane moduli should depend on both electrical and mechanical stress, which would cause an additional mode softening [111]. We hope that combining this effect with nonlocality will be illuminating. 

TMA measures the mechanical response of a polymer looking at (1) expansion properties including the coefficient of linear expansion, (2) tension properties such as measurement of shrinkage and expansion under tensile stress, i.e., elastic modulus, (3) volumetric expansion, i.e., specific volume, (4) single-fiber properties, and (5) compression properties such as measuring the softening or penetration under load. 

Chai Hu can disperse and spread the suppressed Liver-Qi. Xiang Fu can regulate the Liver-Qi and smooth the movement. The sour Bai Shao Yao and sweet Zhi Gan Cao can soften the Liver, ease the tendons and reduce the tension. They are often used in herbal formulas. 

These herbs are selected to relax tendons. Gan Cao is sweet in nature and enters all meridians. It is often used together with sour herbs such as Bai Shao Yao (Paeoniae radix lactiflora) and Mu Gua to generate Yin to soften the Liver, ease the muscles and tendons, relieve cramp and reduce high tension in the body. 

Bai Shao Yao, as deputy, nourishes the Liver-Yin, softens the Liver and reduces the tension of the muscles and tendons when the Liver attacks the Spleen. 

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