Constituent properties

Investigations to find such additive constituent properties of molecules go back to the 1920s and 1930s with work by Fajans [6] and others. In the 1940s and 1950s lhe focus had shifted to the estimation of thermodynamic properties of molecules such as heat of formation, AHf, entropy S°, and heat capacity, C°. 

Constituent property, and related data Ogdensburg, N.Y. Cornwall, Ontario, Canada Ogdensburg, N.Y. Cornwall, Ontario, Canada ... 

The difference between the bounds defined by the simple models can be large, so that more advanced theories are needed to predict the transverse modulus of unidirectional composites from the constituent properties and fiber volume fractions (1). The Halpia-Tsai equations (50) provide one example of these advanced theories ia which the rule of mixtures expressions for the extensional modulus and Poisson s ratio are complemented by the equation... 

Figure 1-23 Translation from Constituent Properties to Lamina to Laminate Properties...

Schwartz, S. E. White, W. H. Trace Atmospheric Constituents. Properties, Transformation and Fates -, J. Wiley and Sons New York, 1983. 

Constituent properties of bainite, 23 280 of martensite, 23 280-281 of pearlite, 23 280 of tempered martensite, 23 281-282 Constrained geometry catalysts, 16 81 20 193... 

Temper designations, magnesium alloy, 75 347-348, 353-354 Tempered martensite, constituent properties of, 23 281-282 Tempering... 

Stedman, D.H., and Shetter, R. (1983) The global budget of atmospheric nitrogen species. In Trace Atmospheric Constituents properties, Transformations, and Fates (Schwartz, S.S., ed.), pp. 411—454, John Wiley, New York. 

All of the CMC properties that govern structural utility and life depend upon the constituent properties (fibers, matrix, interfaces), as well as the fiber architecture. Since the constituents are variables, optimization of the property profiles needed for design and lifing become prohibitively expensive if traditional empirical procedures are used. The philosophy of this article is based on the recognition that mechanism-based models are needed, which allow efficient interpolation between a well-conceived experimental matrix. The emphasis is on the creation of a framework which allows models to be inserted, as they are developed, and which can also be validated by carefully chosen experiments. 

The initial intent of this review is to address the mechanisms of stress redistribution upon monotonic and cyclic loading, as well as the mechanics needed to characterize the notch sensitivity.5 13 This assessment is conducted primarily for composites with 2-D reinforcements. The basic phenomena that give rise to inelastic strains are matrix cracks and fiber failures subject to interfaces that debond and slide (Fig. 1.1).14-16 These phenomena identify the essential constituent properties, which have the typical values indicated in Table 1.1. 

Table 1.1 Constituent properties of CMCs and methods of measurement...

Constituent property Measurement methods Typical range... 

Analyses of damage and failure have established that certain constituent properties are basic to composite performance (Table 1.1). These need to be measured, independently, and then used as characterizing parameters, analogous to the yield strength and fracture toughness in monolithic materials. The... 

The average residual stress in a 0/90 laminate, with uniform laminate thickness, cr, depends on constituent properties in approximate accordance with59,60... 

Note that the residual stress aM — 0 on the elastic properties becomes homogeneous (Ef = Em = EL). While connections between the residual stresses and constituent properties are rigorous, experimental determination is still necessary, because ft is not readily predictable. In general, ft includes terms associated with the thermal expansion difference, ay— am, as well as volume changes that occur either upon crystallization or during phase transformations. For CVI systems, intrinsic stresses may also be present. 

Table 1.3 Important constituent properties for two typical CMCs comparison between SiC/SiC and SiC/CAS...

Analyses of the plastic strains caused by matrix cracks, combined with calculations of the compliance change, provide a constitutive law for the material. The important parameters are the permanent strain, e0 and the unloading modulus, E. These quantities, in turn, depend on several constituent properties the sliding stress, r, the debond energy, T, and the misfit strain, il. The most important results are summarized below. 

Small Debond Energy. For SDE, when cr< crs, the unloading modulus E depends on r0, but is independent of T, and Cl. However, the permanent strain e0 depends on T, and Cl, as well as r0. These differing dependencies of E and e0 on constituent properties have the following two implications. (1) To simulate the stress-strain curve, both e0 and E are required. Consequently, r0, T, and Cl must be known. (2) The use of unloading and reloading to evaluate the constituent properties has the convenience that the hysteresis is dependent only on tq. Consequently, precise determination of r0 is possible. Moreover, with t0 known from the hysteresis, both T,- and Cl can be evaluated from the permanent strain. The principal SDE results are as follows. 

The preceding constitutive laws may be used to simulate stress-strain curves for comparison with experiments. In order to conduct the simulations, the constituent properties, t, T, and ft are first assembled into the non-dimensional parameters9 , 2and 2r. For this purpose, it is necessary to have independent knowledge of d(a). When this does not exist, an estimation procedure is needed, based on Eqn. (45), through evaluation of ds, ermc and a . The first step is to use Eqn. (41) to evaluate the saturation crack spacing ds... 

Fig. l. 27 Simulated stress-strain curves for 1-D CMCs indicating the relative importance of constituent properties. 

It is also possible to estimate dmc from the constituent properties, by using Eqn. (34). Then Eqn. (42) is used to estimate crs. 

When d a) has been established in this manner, stress-strain curves can be simulated for 1-D materials. Based on this approach, simulations have been used to conduct sensitivity studies of the effects of constituent properties on the inelastic strain. Examples (Fig. 1.27) indicate the spectrum of possibilities for CMCs. 

The constituent properties from Table 1.3 can, in turn, be used to simulate the stress-strain curves (Fig. 1.31). The agreement with measurements affirms the simulation capability whenever the constituent properties have been obtained from completely independent tests (Table 1.1). This has been done for the SiC/CAS material, but not yet for SiC/SiC. While the limited comparison between simulation and experiment is encouraging, an unresolved problem concerns the predictability of the saturation stress, crs. In most cases, ab initio determination cannot be expected, because the flaw parameters for the matrix (processing sensitive. Reliance must therefore be placed on experimental measurements, which are rationalized, post facto. Further research is needed to establish whether formalisms can be generated from the theoretical results which provide useful bounds on as. A related issue concerns the necessity for matrix crack density information. Again, additional insight is needed to establish meaningful bounds. Meanwhile, experimental methods that provide crack density information in an... 

The property of principal importance within Wis the shear modulus, G, which reflects the increase in compliance caused by the matrix cracks. However, it remains to develop a model that gives a complete relationship between the composite strength and the constituent properties. 

---