Stress of composite materials

Figure 18. Thermal cycling and irradiation effects on the failure stress of composite materials. (Reproduced from reference 9.)...

Figure 4.13 Distribution curves of the axial stress of composite materials under different interface elastic moduli (fj).

In the stress analysis of composite materials, the parameters are as follows. The elastic modulus of resin matrix = 1.67 GPa, Poisson s ratio = 0.2, yield strength = 3.5 MPa the elastic modulus of the SiC whisker Ef = 410 GPa, Poisson s ratio Vf = 0.17 the exterior stress o is set to 0.8 Mpa and the volume fraction of the whisker in the composite material is 12.5%. The distribution curve of the axial stress of composite material reinforced with whiskers with different L/D ratios is shown in Figure 4.15. In the figure, Zj(//) stands for the axial... 

Figure 4.15 Distribution curve of axial stress of composite material reinforced by whiskers with different L/D ratios.

As shown in Figure 4.15, with an increase of the L/D ratio of whiskers, the distribution curve of the axial stress of composite material moves upward, and the stress borne by whiskers and resins increases. At the same time, the stress borne by the resin matrix changes only slightly. The L/D ratio of the whisker has a significantly greater impact on the whisker stress than on the resin matrix. 

From Table 6.10 we can see that the bending stress of composite materials increases when filled with 5%-20% calcium carbonate whiskers the bending stress of the composite material filled with 5% whiskers increases 23.4% over that of pure PP the fracture bending strain of the composite materials filled with 20%-30% whiskers increases significantly. 

The inherent anisotropy (most often only orthotropy) of composite materials leads to mechanical behavior characteristics that are quite different from those of conventional isotropic materials. The behavior of isotropic, orthotropic, and anisotropic materials under loadings of normal stress and shear stress is shown in Figure 1-4 and discussed in the following paragraphs. 

In Section 2.2, the stress-strain relations (generalized Hooke s law) for anisotropic and orthotropic as well as isotropic materials are discussed. These relations have two commonly accepted manners of expression compliances and stiffnesses as coefficients (elastic constants) of the stress-strain relations. The most attractive form of the stress-strain relations for orthotropic materials involves the engineering constants described in Section 2.3. The engineering constants are particularly helpful in describing composite material behavior because they are defined by the use of very obvious and simple physical measurements. Restrictions in the form of bounds are derived for the elastic constants in Section 2.4. These restrictions are useful in understanding the unusual behavior of composite materials relative to conventional isotropic materials. Attention is focused in Section 2.5 on stress-strain relations for an orthotropic material under plane stress conditions, the most common use of a composite lamina. These stress-strain relations are transformed in Section 2.6 to coordinate systems that are not aligned with the principal material... 

N. J. Pagano and P. C. Chou, The Importance of Signs of Shear Stress and Shear Strain in Composites, Journal of Composite Materials, January 1969, pp. 166-173. 

The average stress acts on cross-sectional area A of the representative volume element, oj acts on the cross-sectional area of the fibers Af, and acts on the cross-sectional area of the matrix A. Thus, the resultant force on the representative volume element of composite material is... 

Definitive studies of composite material tensile strength from a micromechanics viewpoint simply do not exist. Obviously, much work remains in this area before composite materials can be accurately designed, i.e., constituents chosen and proportioned to resist a specified tensile stress. 

R. Byron Pipes and N. J. Pagano, Interiaminar Stresses in Composite Laminates Under Unilorm Axial Extension, Journal of Composite Materials, October 1970, pp. 538-548. 

The objective of this chapter is to address introductory sketches of some fundamental behavior issues that affect the performance of composite materials and structures. The basic questions are, given the mechanics of the problem (primarily the state of stress) and the materials basis of the problem (essentially the state of the material) (1) what are the stiffnesses, (2) what are the strengths, and (3) what is the life of the composite material or structure as influenced by the behavioral or environmental issues in Figure 6-1 ... 

Typical S-N (stress versus number of cycles) curves for various metals and composite materials are shown in Figure 6-4 [6-3]. The boron-epoxy composite material curve is much flatter than the aluminum curve as well as being flatter than the curves for any of the metals shown. The susceptibility of composite materials to effects of stress concentrations such as those caused by notches, holes, etc., is much less than for metals. Thus, the initial advantage of higher strength of boron-epoxy... 

Composite materials have many distinctive characteristics reiative to isotropic materials that render application of linear elastic fracture mechanics difficult. The anisotropy and heterogeneity, both from the standpoint of the fibers versus the matrix, and from the standpoint of multiple laminae of different orientations, are the principal problems. The extension to homogeneous anisotropic materials should be straightfor-wrard because none of the basic principles used in fracture mechanics is then changed. Thus, the approximation of composite materials by homogeneous anisotropic materials is often made. Then, stress-intensity factors for anisotropic materials are calculated by use of complex variable mapping techniques. 

Viscoelastic characteristics of composite materials usually result from a viscoelastic-matrix material such as epoxy resin. General stress analysis of viscoelastic composites was discussed by Schapery [6-54]. An important application to laminated plates was made by Sims [6-55]. 

Jamea M. Wl ey, Stress Analysis of Thick Laminated Composite and Sandvrich Plates, Journal of Composite Materials, October 1972, pp. 426-440. 

R. A. Schapery, Stress Analysis of Viscoelastic Composite Materials, in Composite Materials Workshop, S. W. Tsai, J. C. Hatpin, and Nicholas J. Pagano (Editors), St Louis, Missouri, 13-21 July 1967, Technomic, Westport, Connecticut, 1968, pp. 153-192. Also Journal of Composite Materials, July 1967, pp. 228-267. 

Tsai, H.C., Arocho, A.M. and Cause, L.W. (1990). Prediction of fiber-matrix interphase properties and their influence on interface stress, displacement and fracture toughness of composite materials. Mater. Sci. Eng. A126, 295-304. 

Kim, J.K. and Mai, Y.W, (1996b). Modelling of stress transfer across the fiber-matrix interface. In Numerical Analysis and Modelling of Composite Materials. (J. Bull ed.). Blackie Academic Professional, Glasgow, Ch. 10, pp. 287-326. 

Figure 5.108 Schematic comparison of stress-strain diagrams for common reinforcing fibers (HMG = high modulus graphite) and whiskers. Reprinted, by permission, from A. Kelly, ed.. Concise Encyclopedia of Composite Materials, revised edition, p. 312. Copyright 1994 by Elsevier Science Publishers, Ltd.

The quasielastic method as developed by Schapery [26] is used in the development of the viscoelastic residual stress model. The use of the quasielastic method is motivated by the fact that the relaxation moduli are required in the viscoelastic analysis of residual stresses, whereas the experimental characterization of composite materials is usually in terms of the creep compliances. An excellent account of the development of the quasielastic method is given in [27]. The underlying restriction in the application of the quasielastic method is that the compliance response of the material shows little curvature when plotted versus log time [28]. Harper [27] shows excellent agreement between the quasielastic method and direct inversion for AS4/3510-6 graphite/epoxy composite. For most graphite/thermoset systems, the restrictions imposed by the quasielastic method are satisfied. 

Mechanical testing of the three-step cure specimens indicated that no sacrifice in properties resulted from the modification of the process cycle. The retainment of mechanical properties (transverse strength and modulus) coupled with the reduction in dimensionless curvature for the three-step cure cycles investigated provides another suitable cure cycle modification for reduction of residual stresses in composite materials. Overall processing time has not been increased beyond that specified in the MRC cycle. Thus, with no increase in process time and comparable mechanical properties, the residual stresses have been reduced by more than 20 percent in comparison to the MRC cycle baseline data. 

Some materials might produce a unique failure surface providing measurements could be conducted under first stretch conditions in a state of equilibrium. Tschoegl (110), at this writing, is attempting to produce experimental surfaces by subjecting swollen rubbers to various multiaxial stress states. The swollen condition permits failure measurements at much reduced stress levels, and the time dependence of the material is essentially eliminated. Studies of this type will be extremely useful in establishing the foundations for extended efforts into failure of composite materials. 

This new book focuses on the fundamental understanding of composite materials at the microscopic scale, from designing microstructural features, to the predictive equations of the functional behaviour of the stmcture for a specific end-application. The papers presented discuss stress and temperature-related behavioural phenomena based on knowledge of physics of microstructure and microstructural change over time. 

---