Strain at fracture

Forming Limit Analysis. The ductihty of sheet and strip can be predicted from an analysis that produces a forming limit diagram (ELD), which defines critical plastic strains at fracture over a range of forming conditions. The ELD encompasses the simpler, but limited measures of ductihty represented by the percentage elongation from tensile tests and the minimum bend radius from bend tests. 

The plastic strain at fracture decreases markedly with time as the cement ages also the elastic modulus increases (Wilson, Paddon Crisp, 1979 Barton et al., 1975). There is an increase in dynamic modulus with time (Barton et al., 1975). 

The tensile curve of a polymer fibre is characterised by the yield strain and by the strain at fracture. Both correspond with particular values of the domain shear strain, viz. the shear yield strain j =fl2 with 0.04rotation angle of -0y=fl2 and the critical shear strain 0-0b=/iwith /f=0.1. For a more fundamental understanding of the tensile deformation of polymer fibres it will be highly interesting to learn more about the molecular phenomena associated with these shear strain values. 

Texture has a number of component attributes, and some of them can be assessed by mechanical means. The texture or firmness of cooked potatoes is evaluated by subjecting each sample to a compression test using a universal testing machine equipped with a load cell. Cooked potato cylinders are compressed in a single-cycle compression-decompression test. Uniaxial compression is measured with an Instron machine with a lOON load cell. Measurements are performed on hot potato cylinders (depth 12 mm, height 10 mm) from 15 potatoes immediately after cooking, at a deformation rate of 20 mm/min. Stress and strain at fracture are calculated by the Instron series IX version 7.40 software and means of 15 repetitions are calculated. 

Sharma (90) has examined the fracture behavior of aluminum-filled elastomers using the biaxial hollow cylinder test mentioned earlier (Figure 26). Biaxial tension and tension-compression tests showed considerable stress-induced anisotropy, and comparison of fracture data with various failure theories showed no generally applicable criterion at the strain rates and stress ratios studied. Sharma and Lim (91) conducted fracture studies of an unfilled binder material for five uniaxial and biaxial stress fields at four values of stress rate. Fracture behavior was characterized by a failure envelope obtained by plotting the octahedral shear stress against octahedral shear strain at fracture. This material exhibited neo-Hookean behavior in uniaxial tension, but it is highly unlikely that such behavior would carry over into filled systems. 

Abbrevia- tion E-modulus (short-term) Tensile strength (short-term) Strain at fracture Notched impact strength... 

If for the polymer fibre in Example 13.7 the fracture stress of is equal to 3.35 GPa (see Fig. 13.102), then estimate the orientation at fracture and the strains at fracture due to stretching and to chain rotation. 

Fig. 34. Influence of morphology (f, = content of coarsespherulites) on band initiation stress, and strain at fracture,...

The main problem is related to exposure of these materials to high temperatures in the presence of oxygen. These conditions favor the oxidative degradation of the elastomer, which leads to opposing changes in its structure. On the one hand, chain scission can occur, and on the other hand, cross-links can be generated. If chain scission dominates, the hardness and modulus of the elastomer will decrease. If, however, cross-links are generated, both the hardness and the modulus increase and the strain at fracture will decrease. Other mechanical properties are altered by an increase in... 

FIGURE 17.8 Fracture behavior of two cylindrical cheese samples subjected to uniaxial compression. Sample (1) concerns a hard and fairly brittle cheese, (2) a semihard green cheese that is quite extensible, (a) Stress a versus Hencky strain eH, resulting upon deformation at a strain rate W of 1CT2 s 1 the dotted lines indicate the strain at fracture fr. (b) Values of Sfr obtained at various W. (c) Fracture mode as seen in cross sections through the test pieces at the moment of maximum stress for (1) it is a vertical cross section, for (2) a horizontal one. 

This also plays a part in large deformation and fracture. Before fracture occurs, the stress-carrying strands have become stretched. That means that Eq. (17.18) can also be used for the fracture stress with a = 2, albeit with a very different value for K . The strain at fracture fr will strongly depend on the deformability of the primary particles it will also be larger for a smaller value of cp. 

All materials tend to fracture if stressed severely enough. Some materials fracture more easily than others, and are thereby said to be brittle . Brittleness is the property of a material manifested by fracture without appreciable prior plastic deformation. In ductile fracture significant plastic flow occurs before fracture. Strain at fracture is more than a few per cent, unlike brittle fracture, and may be several hundred per cent. However, a sharp distinction cannot be made between brittle and ductile fracture since even in glassy materials some deformations take place. Further, a given material will fail in a brittle manner under some conditions and a ductile manner under other conditions. Thus, brittle fracture is favored by the low temperature, fast loading and when the state of stress approaches a uniform, i.e., triaxial or dUatational, state. Materials with low T are more... 

The strain at fracture of film samples can be calculated within the framework of a cluster model of polymers amorphous state structure [205] ... 

J Mechanical testing parameters (a) A representative strain-stress curve in tensile testing. Yield stress (o-yg) and yield point strain (eyp) can be obtained by recording values at the point where the curve transitions from a linear relationship between stress and strain (elastic deformation) to a non-linear relationship (plastic deformation). Ultimate tensile strength (fr ,s) is the maximum stress in the curve, and the corresponding strain is called uniform strain (cp). The strain at fracture (eO can also be obtained from the curve, (b) When the transition point between elastic and plastic deformation is difficult to identify, a 0.2% strain offset line parallel to the elastic portion is drawn to obtain the <7ys or 0.2% offset o-ys. (c) Schematic of the deformation that occurs when shear force is applied to a viscoelastic polymer. 

A region of rather intense acoustical activity occurred at the yield point, followed by a quieter region until a shear strain of about 1.5 was reached. At this point there was a rather abrupt increase in acoustical activity that continued to the strain at fracture which was appreciably greater than 1.5. 

The curve of the monolith consists of primary, steady-state and very small tertiary creep. The specimen lifetime was 150 h and 4 % of creep strain was obtained at fracture. A large number of microcracks were also identified by optical microscopy. Compared to the monolith, the nanocomposite exhibited excellent creep resistance. At 1200 °C and 50 MPa, its creep hfe was 1120 h, which is 10 times longer than that of the monolith. The creep strain at fracture was 0.5 %, which is eight times smaller than that of the monohth. Furthermore, the superior creep resistance of the nanocomposite was also obtained by flexure creep tests. Similar to tensile-creep curves, the strain of the nanocomposite tended to decrease over time, while the monolith exhibited steady-state creep and sometimes accelerated creep. 

The initial slopes of the curves were used to compute tensile moduli. The maximum stress reached during a run was used to calculate tensile strength, and the strain at fracture was taken as the ultimate elongation. The yield point was defined as the intercept of the stress-strain curve with a straight line parallel to the initial slope and offset 0.2% extension. The tensile data taken at 293, 77, and 4.2 K are summarized in Tables III, IV, and V, respectively. 

---