Tensile stress growth coefficient

The maximum strain rate (e < Is1) for either extensional rheometer is often very slow compared with those of fabrication. Fortunately, time-temperature superposition approaches work well for SAN copolymers, and permit the elevation of the reduced strain rates kaj to those comparable to fabrication. Typical extensional rheology data for a SAN copolymer (h>an = 0.264, Mw = 7 kg/mol,Mw/Mn = 2.8) are illustrated in Figure 13.5 after time-temperature superposition to a reference temperature of 170°C [63]. The tensile stress growth coefficient rj (k, t) was measured at discrete times t during the startup of uniaxial extensional flow. Data points are marked with individual symbols (o) and terminate at the tensile break point at longest time t. Isothermal data points are connected by solid curves. Data were collected at selected k between 0.0167 and 0.0840 s-1 and at temperatures between 130 and 180 °C. Also illustrated in Figure 13.5 (dashed line) is a shear flow curve from a dynamic experiment displayed in a special format (3 versus or1) as suggested by Trouton [64]. The superposition of the low-strain rate data from two types (shear and extensional flow) of rheometers is an important validation of the reliability of both data sets. 

Figure 13.5 Dependences of the reduced tensile stress growth coefficient ti (i,t)/ar at 170°C on reduced time fay and reduced strain rate iaj for a SAN resin (wAN = 0.264, Mw = 78 kg/mol, Mw/M = 2.8) during the startup of uniaxial extensions flow. Also illustrated (dashed curve) are dynamic shear viscosity data displayed as 3 r7 (c<, 170°C) versus or7 as suggested by Trouton [64]. Reproduced from L. Li, T. Masuda and M. Takahashi, J.Rheol., 34(1), 103(1990), with permission of the American Institute of Physics...

Figure 8. Tensile stress-growth coefficient of sample SI at 123 °C...

Out-of-phase component of complex viscosity Shear stress growth coefficient Shear stress decay coefficient Tensile stress growth coefficient Tensile stress decay coefficient... 

If a filament or rod of a virgin (stress-free) material is stretched at a constant extension rate, the total stress component ajj, initially zero, will increase with time in a manner which depends on the nature of the polymer. It is then possible to define a tensile stress growth coefficient ... 

Hence, for Newtonian liquids, the tensile stress growth coefficient is a constant quantity and the extensional viscosity is three times the shear viscosity. This result was verified experimentally in 1906 by TroutonOD and is known as Trouton s rule. In addition, the ratio of the extensional viscosity to the shear viscosity is known as Trouton s ratio. 

Vinogradov et used a more sophisticated setup compared to that of Cogswell, and showed the equivalence of extensional viscosity data obtained using a constant stretch rate instrument and a constant stress instrument for molten polystyrene. An unexpected feature of the constant stress results was that the strain rate was found to decrease initially, as expected, but it then exhibited a minimum before becoming constant. This implies a maximum in the tensile stress growth coefficient and, in that respect, this behavior was similar to that of linear low density polyethylene as reported by Schlund and Utracki< ) among others. 

The material function usually reported in extensional flow rheometry is the tensile stress growth coefficient defined by Eq. 10.92. 

Melt behavior has been studied using uniaxial (also called simple or tensile), biaxial, and planar extensional flows [9, Ch. 6]. However, only the first two of these are in general use and will be discussed here. A uniaxial extensional rheometer is designed to generate a deformation in which either the net tensile stress Tg or the Hencky strain rate e (defined by Eq. 10.89) is maintained constant. The material functions that can, in principle, be determined are the tensile stress growth coefficient / (f, ), the tensile creep compliance, andthetensile... 

Figure 11.14 Tensile stress growth coefficients of (a) a polystyrene (PS) melt of weight average molecular weight = 423,000 and M /M = 2.36 and (b) the same melt mixed with a low percentage (1.5%) of an ultra high molecular weight (UHMW) polystyrene with = 3,220,000...

Figure 11.16 Tensile stress growth coefficients of polydisperse polystyrene samples of Minegishi et al.

For constant-stretch-rate homogeneous deformation, which begins from rest, a tensile stress growth coefficient is defined as... 

Elongational or tensile viscosity Biaxial extensional viscosity Biaxial stress growth coefficient Biaxial stress decay coefficient Scattering angle... 

A coefficient of thermal expansion (CTE) mismatch is present between the Nicalon fibers (4.0 x 10 /°C between 0 and 900°C) and aluminum oxide matrix (8 x 10 /°C between RT and 1000"C). This mismatch leads to the development ofresidual tensile stresses in the matrix on cool down from matrix growth temperatures. In 2-D woven composites, relatively larger areas of unreinforced matrix are likely to occur between fabric plies. Hence, for 2-D Nicalon /AI2O3 composites, these unreinforced regions are likely to develop residual tensile stresses. In some cases, the residual tensile stresses are high enough to cause matrix microcracking. The presence of these microcracks is apparent in Fig. 2. 

The numerical results obtained from simultaneous integration of (1) and (7) are shown in figs 1—3 for a planar cavity cluster at Pm = 20-103 Pa with f = a /27r = 20 kHz when = 0.3 mm. It is apparent from fig. 1 that initially the tensile stress in the cluster drops exponentially with the distance from the cluster boundary [1], but after 4 fjs the pressure profile steepens near the boundary due to the significant growth of the cavities here. The tensile stress decays beyond the first few cavity "layers" where growth of the cavities primarily occurs. The profile of increase of cavity radius vs. position is found to be essentially exponential, fig. 2. The pressure assumed from (15) is set up if an incident acoustic wave with a pressure Api vs. time t as shown in fig. 3 reaches the cluster boundary. It is noticed that very quickly the reflection coefficient approaches —1, showing that the boundary becomes an essentially compliant interface. 

Residual film stress (film formation) The residual compressive or tensile stress in a film that results from the growth process (growth stress), phase change, and/or differences in the coefficients of thermal expansion of the film and substrate (thermal stress). Not a function of film thickness. Can vary through the thickness of the film and be anisotropic with direction in the film. See also Total film stress. 

Figure 17. Biaxial flexural strength, as a function of stress rate (a) and predicted flexural strength as a function of time to fracture (b) for UST dental porcelain, with and without ion exchange, in artificial saliva at 37°C. In a),(Jjo is the scaling parameter and n is the slow crack growth, SCG, susceptibility coefficient. Inert strength was determined at 100 MPa/s in air with a drop of silicone oil on the tensile surface to inhibit the occurrence of SCG. In (b), the slope of fitted curve is related with n. Data from [63,71]...

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