Stress-strain behavior ceramics

The strength of the fiber-matrix interface is one of the key parameters responsible for the stress-strain behavior and damage tolerance of ceramic composites. Two different types of tests are available to measure the fiber-matrix interfacial properties in fiber-reinforced ceramic composites. The first is based on an indentation technique to either push the individual fiber into or through the matrix. The second test method relies on pulling a single fiber out of a matrix. These methods have been compared59 to one another for a glass matrix material, and yield similar results. 

Stress is related to strain through constitutive equations. Metals and ceramics typically possess a direct relationship between stress and strain the elastic modulus (2) Polymers, however, may exhibit complex viscoelastic behavior, possessing characteristics of both liquids and solids (4.). Their stress-strain behavior depends on temperature, degree of cure, and thermal history the behavior is made even more complicated in curing systems since material properties change from a low molecular weight liquid to a highly crosslinked solid polymer (2). ... 

The stress-strain behavior of ceramic polycrystals is substantially different from single crystals. The same dislocation processes proceed within the individual grains but these must be constrained by the deformation of the adjacent grains. This constraint increases the difficulty of plastic deformation in polycrystals compared to the respective single crystals. As seen in Chapter 2, a general strain must involve six components, but only five will be independent at constant volume (e,=constant). This implies that a material must have at least five independent slip systems before it can undergo an arbitrary strain. A slip system is independent if the same strain cannot be obtained from a combination of slip on other systems. The lack of a sufficient number of independent slip systems is the reason why ceramics that are ductile when stressed in certain orientations as single crystals are often brittle as polycrystals. This scarcity of slip systems also leads to the formation of stress concentrations and subsequent crack formation. Various mechanisms have been postulated for crack nucleation by the pile-up of dislocations, as shown in Fig. 6.24. In these examples, the dislocation pile-up at a boundary or slip-band intersection leads to a stress concentration that is sufficient to nucleate a crack. 

Figure 17.7a shows the stress-strain behavior for a single crystal that is favorably oriented for plastic flow. This type of behavior is seen in MgO and other ceramics with a rocksalt structure. There are three distinct stages ... 

FIGURE 2. Typical tensile stress-strain behaviors measured on 2-D SiC/SiC composites possessing PyC based interphases and fabricated from untreated ortreated Nicalon (ceramic grade) fibers (a) strong fiber/coating interfaces... 

The cellular micro- and macrostructure pseudomorphs with naturally grown wood tissue show a complex mechanical behavior, which is governed hy the unique arrangement of cells. In some aspects, the fracture behavior in biomorphous ceramics is similar to that of fibrous monolithic ceramics, as well as that of laminate composite ceramics showing a noncatastrophic stress-strain behavior. A pronounced anisotropy of fracture behavior is a characteristic feature which depends on the loading conditions with respect to the orientation of the cell-packing structure [357]. 

Fig. 7.40 Tensile stress-strain behavior, the cyclic curves are for a stress ratio, R of 0.1 and a frequency of 0.1 Hz at room temperature, a The submicron sized 3Y-TZP ceramics (0.35 pm) showing cyclic hardening, b the nanocrystalline 3Y-TZP ceramics (100 nm) showing cyclic softening [37]. With kind permission of John Wiley and Sons...

The addition of continuous fibers to a ceramic matrix can significantly change the failure mode. Monolithic ceramics have linear stress-strain curves and fail catastrophically at low strain levels. However, CMCs display nonlinear stress-strain behavior with much more area under the curve, indicating that more energy is absorbed during failure and that the material has a less catastrophic failure mode. 

Figure 12.11 Stress—strain behavior of continuous fiber-reinforced matrix in ceramic composites [78].

Here, y is the surface energy. Until fracture, the ceramics are in an elastic state. Hence, Hooke s law is applicable for their stress-strain behavior. This... 

Materials are frequently chosen for structural applications because they have desirable combinations of mechanical characteristics. The present discussion is confined primarily to the mechanical behavior of metals polymers and ceramics are treated separately because they are, to a large degree, mechanically different from metals. This chapter discusses the stress-strain behavior of metals and the related mechanical properties, and also examines other important mechanical characteristics. Discussions of the microscopic aspects of deformation mechanisms and methods to strengthen and regulate the mechanical behavior of metals are deferred to later chapters. 

Figore 12.30 A three-point loading scheme for measuring the stress-strain behavior and flexnral strength of brittle ceramics, inclnding expressions for compnting stress for rectangnlar and circular cross sections. 

The stress-strain behaviors and fracture strengths of ceramic materials are determined using transverse bending tests. 

The stress-strain curves for cortical bones at various strain rates are shown in Figure 5.130. The mechanical behavior is as expected from a composite of linear elastic ceramic reinforcement (HA) and a compliant, ductile polymer matrix (collagen). In fact, the tensile modulus values for bone can be modeled to within a factor of two by a rule-of-mixtures calculation on the basis of a 0.5 volume fraction HA-reinforced... 

Background At elevated temperatures the rapid application of a sustained creep load to a fiber-reinforced ceramic typically produces an instantaneous elastic strain, followed by time-dependent creep deformation. Because the elastic constants, creep rates and stress-relaxation behavior of the fibers and matrix typically differ, a time-dependent redistribution in stress between the fibers and matrix will occur during creep. Even in the absence of an applied load, stress redistribution can occur if differences in the thermal expansion coefficients of the fibers and matrix generate residual stresses when a component is heated. For temperatures sufficient to cause the creep deformation of either constituent, this mismatch in creep resistance causes a progres-... 

In some cases, an extrudable and injectable paste may consist of 65% vol. ceramic powder and 35% vol. polymeric binder. In others, an extrudable paste may consist of a highly loaded aqueous suspension of clay particles such that its rheology is plastic. Hie low shear (i.e., <100 sec ) viscosity of such a paste is between 2000 and 5000 poise at ambient temperature. Highly nonlinear stress strain curves are typical of ceramic pastes, as well as time dependent thixotropy. In many cases, pastes behave like visco-elastic fluids. This complex rheological behavior of ceramic pastes has made theoretical approadies to these problems difficult. For this reason, the discussion in this chapter is limited to Newtonian fluids where analytical solutions are possible, with obvious consequences as to accuracy of these equations for non-Newtonian ceramic pastes. 

FIGURE 12.11 Improvements of the mechanical properties of three-dimensional reinforced CMCs by hybrid infiltration routes (a) R.T. flexural stress-strain plots for a three-dimensional carbon fiber reinforced composite before and after cycles of infiltration (comparison between eight cycles with zirconium propoxide and fonr cycles pins a last infiltration with aluminum-silicon ester (b) plot of the mechanical strength as a fnnction of the final open porosity for composites and matrix of equivalent porosity, before and after infiltration (Reprinted from Colomban, R and Wey, M., Sol-gel control of the matrix net-shape sintering in 3D reinforced ceramic matrix composites, J. Eur. Ceram. Soc., 17, 1475, 1997. With permission from Elsevier) (c) R.T. tensile behavior (d) comparison of the R.T. mechanical strength after thermal treatments at various temperatures. (Reprinted from Colomban, R, Tailoring of the nano/microstructure of heterogeneous ceramics by sol-gel routes, Ceram. Trans., 95, 243, 1998. With permission from The American Ceramic Society.)... 

The deformation behavior of a compositionally graded metal-ceramic structure has been investigated by numerical and (semi)analytical simulations. Random microstructure models are able to predict the response of an FGM-structure in a more accurate way than the other approaches. The interwoven structure in the middle of the FGM can be accounted for using this modeling strategy. For the extended periodic unit cell models the predicted stress strain response depends strongly on the micro-arrangement of the inclusions. Detailed information on the microfields of the stresses and strains can only be obtained by the extended unit cell models. The incremental Mori-Tanaka method... 

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