Editing Compressive strength (section)

== Compressive failure modes ==
[[File:Universal Testing Machine.jpg|thumb|right|A cylinder being crushed under a UTM]]
If the ratio of the length to the effective radius of the material loaded in compression ([[Slenderness ratio]]) is too high, it is likely that the material will fail under [[buckling]]. Otherwise, if the material is ductile yielding usually occurs which displaying the barreling effect discussed above. A brittle material in compression typically will fail by axial splitting, shear fracture, or ductile failure depending on the level of constraint in the direction perpendicular to the direction of loading.  If there is no constraint (also called confining pressure), the brittle material is likely to fail by axial splitting. Moderate confining pressure often results in shear fracture, while high confining pressure often leads to ductile failure, even in brittle materials.<ref>{{Cite book|last=Fischer-Cripps|first=Anthony C. |title=Introduction to contact mechanics|date=2007|publisher=Springer|isbn=978-0-387-68188-7|edition=2nd|location=New York|page=156|oclc=187014877}}</ref>

Axial Splitting relieves elastic energy in brittle material by releasing strain energy in the directions perpendicular to the applied compressive stress. As defined by a materials [[Poisson's ratio|Poisson ratio]] a material compressed elastically in one direction will strain in the other two directions. During axial splitting a crack may release that tensile strain by forming a new surface parallel to the applied load. The material then proceeds to separate in two or more pieces. Hence the axial splitting occurs most often when there is no confining pressure, i.e. a lesser compressive load on axis perpendicular to the main applied load.<ref>Ashby, M., and C. Sammis. “The Damage Mechanics of Brittle Solids in Compression.” ''Pure and Applied Geophysics'', vol. 133, no. 3, 1990, pp. 489–521., doi:10.1007/bf00878002.</ref> The material now split into micro columns will feel different frictional forces either due to inhomogeneity of interfaces on the free end or stress shielding. In the case of [[stress shielding]], inhomogeneity in the materials can lead to different [[Young's modulus]]. This will in turn cause the stress to be disproportionately distributed, leading to a difference in frictional forces. In either case this will cause the material sections to begin bending and lead to ultimate failure.<ref>Renshaw, Carl E., and Erland M. Schulson. “Universal Behaviour in Compressive Failure of Brittle Materials.” ''Nature'', vol. 412, no. 6850, 2001, pp. 897–900., doi:10.1038/35091045.</ref>

=== Microcracking ===
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[[File:Customhw406figure.jpg|thumb|Figure 1: microcrack nucleation and propagation]]Microcracks are a leading cause of failure under compression for [[brittle]] and quasi-brittle materials. Sliding along crack tips leads to tensile forces along the tip of the crack. Microcracks tend to form around any pre-existing crack tips. In all cases it is the overall global compressive stress interacting with local microstructural anomalies to create local areas of tension.  Microcracks can stem from a few factors.

# Porosity is the controlling factor for compressive strength in many materials. Microcracks can form around pores, until about they reach approximately the same size as their parent pores. (a)
# Stiff inclusions within a material such as a precipitate can cause localized areas of tension. (b) When inclusions are grouped up or larger, this effect can be amplified.
# Even without pores or stiff inclusions, a material can develop microcracks between weak inclined (relative to applied stress) interfaces. These interfaces can slip and create a secondary crack. These secondary cracks can continue opening, as the slip of the original interfaces keeps opening the secondary crack (c). The slipping of interfaces alone is not solely responsible for secondary crack growth as inhomogeneities in the material's [[Young's modulus]] can lead to an increase in effective misfit strain. Cracks that grow this way are known as wingtip microcracks.<ref>Bažant, Zdeněk P., and Yuyin Xiang. “Size Effect in Compression Fracture: Splitting Crack Band Propagation.” ''Journal of Engineering Mechanics'', vol. 123, no. 2, Feb. 1997, pp. 162–172., doi:10.1061/(asce)0733-9399(1997)123:2(162).</ref>

The growth of microcracks is not the growth of the original crack or imperfection. The cracks that nucleate do so perpendicular to the original crack and are known as secondary cracks.<ref name="auto">Horii, H., and S. Nemat-Nasser. “Compression-Induced Microcrack Growth in Brittle Solids: Axial Splitting and Shear Failure.” ''Journal of Geophysical Research'', vol. 90, no. B4, 10 Mar. 1985, p. 3105., doi:10.1029/jb090ib04p03105.</ref> The figure below emphasizes this point for wingtip cracks.
These secondary cracks can grow to as long as 10-15 times the length of the original cracks in simple (uniaxial) compression. However, if a transverse compressive load is applied. The growth is limited to a few integer multiples of the original crack's length.<ref name="auto"/>[[File:Wingtipmicrocrack.jpg|thumb|A secondary crack growing from the tip of a preexisting crack|left|183x183px]][[File:Shear band.jpg|thumb|shear band formation]]

==== Shear bands ====
If the sample size is large enough such that the worse defect's secondary cracks cannot grow large enough to break the sample, other defects within the sample will begin to grow secondary cracks as well. This will occur homogeneously over the entire sample. These micro-cracks form an echelon that can form an “intrinsic” fracture behavior, the nucleus of a shear fault instability. Shown right:

Eventually this leads the material deforming non-homogeneously. That is the strain caused by the material will no longer vary linearly with the load. Creating localized [[shear band]]s on which the material will fail according to deformation theory. “The onset of localized banding does not necessarily constitute final failure of a material element, but it presumably is at least the beginning of the primary failure process under compressive loading.”<ref>Fracture in Compression of Brittle Solids. The National Academies Press, 1983, doi:10.17226/19491.</ref>