Poisson plastic

The modulus term in this equation can be obtained in the same way as in the previous example. However, the difference in this case is the term V. For elastic materials this is called Poissons Ratio and is the ratio of the transverse strain to the axial strain (See Appendix C). For any particular metal this is a constant, generally in the range 0.28 to 0.35. For plastics V is not a constant. It is dependent on time, temperature, stress, etc and so it is often given the alternative names of Creep Contraction Ratio or Lateral Strain Ratio. There is very little published information on the creep contraction ratio for plastics but generally it varies from about 0.33 for hard plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are given in Table 2.1 but do remember that these may change in specific loading situations. 

If we take the critical stress as the yield stress then for many plastics, the ratio of adE is approximately 35 x 10 2. Using Poisson s ratio, v = 0.35 and taking p = 0.6, as before, then... 

The Cenozoic portions of the Gulf Coast sedimentary basins are immature therefore, little cementing of the sediments has taken place. Poisson s ratio varies with depth for such sedimentary columns, reflecting the variation of properties through the column. At great depth (i.e., approaching 20,000 ft), Poisson s ratio approaches that of incompressible, plastic materials (i.e., 0.5) [35]. 

Poisson s ratio always falls within the range of 0 to 0.5. A zero value indicates that the specimen would suffer no reduction in diameter or contraction laterally during elongation but would undergo a reduction in density. A value of 0.5 indicates that the specimen s volume would remain constant during elongation or as the diameter decreases. For most plastics the ratio lies between 0.10 and 0.40 (Tables 2-1 and 2-2). 

Table 2-2 Examples of specific room temperature shear stress-strain data and Poisson s ratio for several plastics and other materials...

The load or stress has another effect on the creep behavior of most plastics. The volume of isotropic or amorphous plastic increases as it is stretched unless it has a Poisson ratio of 0.50. At least part of this increase in volume manifests itself as an increase in free volume and a simultaneous decrease in viscosity. This decrease in turn shifts the retardation times to being shorter. 

Ep = MODULUS OF ELASTICITY OF PLASTIC Em = MODULUS OF ELASTICITY OF METAL vp = POISSON S RATIO OF PLASTIC... 

The behavior of the strain softened material resembles the behavior of rubberlike polymers. For instance, the Poisson s ratio of an ideally plastic material is also close to 0.5 [94, 95], Proper understanding of crack propagation involves the microscopic level. Apparently, the load is transmitted by the molecular strands [97] from one crosslink to the next crosslink, exactly, as it is in rubberlike materials. However, two things are different in strain softened polymers as compared to rubberlike materials ... 

At the instant of contact between a sphere and a flat specimen there is no strain in the specimen, but the sphere then becomes flattened by the surface tractions which creates forces of reaction which produce strain in the specimen as well as the sphere. The strain consists of both hydrostatic compression and shear. The maximum shear strain is at a point along the axis of contact, lying a distance equal to about half of the radius of the area of contact (both solids having the same elastic properties with Poisson s ratio = 1/3). When this maximum shear strain reaches a critical value, plastic flow begins, or twinning occurs, or a phase transformation begins. Note that the critical value may be very small (e.g., in pure simple metals it is zero) or it may be quite large (e.g., in diamond). 

The material properties used in the simulations pertain to a new X70/X80 steel with an acicular ferrite microstructure and a uniaxial stress-strain curve described by er, =tr0(l + / )", where ep is the plastic strain, tr0 = 595 MPa is the yield stress, e0=ff0l E the yield strain, and n = 0.059 the work hardening coefficient. The Poisson s ratio is 0.3 and Young s modulus 201.88 OPa. The system s temperature is 0 = 300 K. We assume the hydrogen lattice diffusion coefficient at this temperature to be D = 1.271x10 m2/s. The partial molar volume of hydrogen in solid solution is... 

The Poisson s ratio (A//Aw, where A/ is the change in length produced by a change of width, Aw) of an isotropic liquid is 0.5, and that of an elastic solid is about 0.2. The value of P for an elastomer, such as NR, is 0.5, and this value decreases as the elastomer is cured with increasing amounts of sulfur, i.e., as the crosslink density increases. Likewise, P for rigid PVC is about 0.3, and this value increases progressively as the plasticizer content is increased. 

It can be proved from Eq. (2.156) that, for materials with Poisson s ratio of 0.3 (which is true for most solids), the maximum shear stress oz — or occurs at z/rc = 0.48. Consequently, according to Tresca s criterion, the yield stress Y in a simple compression is 0.62 p0. Therefore, when the hardness or the yield stress Y of the particle material is less than 0.62 times the maximum contact pressure, the sphere will, most likely, undergo plastic deformation. From the elastic collision of two solid spheres, the maximum contact pressure is given by Eq. (2.134). Thus, the relation between the critical normal collision velocity, Ui2Y. and the yield stress is given by... 

A sharp central crack of length 30 mm in a wide, thick plate of a glassy plastic commences to propagate at Poisson constant = 0.4 and (c) will a crack of length 5 mm in a similar sheet fracture under a tensile stress of 10 MPa ... 

Where Gp and GF are the shear moduli of the plastic matrix and the filler respectively, v is Poisson s ratio of the matrix, and V is the volume fraction. E s are Young s moduli. Recently this relation was verified for the rubber-reinforced thermoplastics (29). The effect of adhesion at the rubber-resin (or rubber-filler) interface has been studied (49, 57, 58) with mathematical models. 

Photocrosslinking 61-77 Photoinitiators 63 f., 69 Physical aging 132 Plasticity at the crack tip 135 Plastic zone 135 Poisson distribution 21 Polyaddition, irreversible step 18 Polyamines, addition to polyepoxides 25 f. Polycarboxylic acids 47 Polyepoxides and polyamines 25 f. Polyepoxy-polyamine systems, multicomponent 36... 

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