Permeability
It is one of the physical properties which is an average (or macroscopic) medium property that measure the ability of the porous medium to transmit fluid through it.
In 1856, Darcy first developed the equation to describe fluid flow through a porous media. Q= - (KA/µ) * (dP/dx)
Q = Volumetric Flow (cm3/s)
K = permeability (Darcy s), (cm2 x cP)/(sec.x atm))
A = cross-sectional area (cm2)
? = viscosity (centipoises (cP))
P = pressure (atm); x = length (cm)
Mechanical Testing
The classical view of ceramic materials includes the following:
1. They are brittle.
2. Dislocations are not important because they do not move.
3. They are polycrystalline and fracture along grain boundaries.
Once again the classical view of ceramics and many of our preconceived ideas of how they behave are not always correct. The modern view of ceramics is therefore very different:
1. We may be using the ceramic as a thin film where stresses may be very high.
2. Deformation at high temperatures may be important.
3. In some special “new” ceramics, displacive transformations become important.
Figure A shows (s–e)? curves for three different materials at room temperature.
Material I: This has a high Young’s modulus, high failure stress, low ductility, low toughness, and fractures without significant plastic deformation. This behavior is characteristic of many ceramics.
Material II: This has moderate strength, moderate ductility, deforms plastically prior to failure, and is the toughest of the three. This behavior is characteristic of many metals.
Material III: This has a low Young’s modulus, is very ductile, and has low ultimate tensile strength and limited toughness. This behavior is characteristic of many elastomers.
The strength of ceramics is affected by many factors, and this complexity is illustrated in Figure B The composition and microstructure are particularly significant and mechanical properties depend strongly on these characteristics.
Figure C shows two specific examples that illustrate the role of microstructure on the strength of ceramics.
16.3 ELASTIC CONSTANTS AND OTHER “CONSTANTS”
In this section we will define some of the parameters that describe the mechanical behavior of materials. Some of these parameters are constants, like Young’s modulus E. Some, like hardness, are not. Hardness depends on how the material was tested.
These are four constants that are most common.
1- E—Young’s modulus (also referred to as the elastic modulus) is a material constant defined by Eq. 1 for a linear elastic material under uniaxial tensile or compressive stress.
EFFECT OF MICROSTRUCTURE ON ELASTIC MODULI
In real ceramics we have to consider the fact that we often have more than one phase present. The overall modulus is then going to be a combination of the properties of each of the phases; it lies somewhere between the high- and low-modulus components. Analytical expressions that represent the upper and lower bounds for Young’s modulus include the following.
TEST TEMPERATURE
Mechanical properties often show strong variations with temperature. The change with temperature may be more abrupt than the gradual decrease in E with increasing temperature. Do ceramics experience a ductile-to-brittle (or the converse) transition and is it important? Ceramics can exhibit both types of behavior over different temperature ranges. Figure D illustrates the temperature dependence of strength for ceramics.
_ Region A: the fracture is brittle and the fracture strain is ~10?3. There is no significant plastic deformation prior to failure and the strength varies little with temperature.
_ Region B: the fracture is again brittle but slight plastic deformation occurs prior to failure. The failure strain is usually in the region 10?3–10?2and strength falls with increasing temperature.
_ Region C: Appreciable plastic flow occurs, with strains of the order of 10?1prior to failure. This behavior is rarely observed in ceramics, even in ductile polycrystalline
ceramics.
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