Compressive strength
In mechanics, compressive strength is the capacity of a material or structure to withstand loads tending to reduce size. It is opposed to tensile strength which withstands loads tending to elongate, resisting tension. In the study of strength of materials, compressive strength, tensile strength, and shear strength can be analyzed independently.
Some materials fracture at their compressive strength limit; others deform irreversibly, so a given amount of deformation may be considered as the limit for compressive load. Compressive strength is a key value for design of structures.
Compressive strength is often measured on a universal testing machine. Measurements of compressive strength are affected by the specific test method and conditions of measurement. Compressive strengths are usually reported in relationship to a specific technical standard.
Introduction
When a specimen of material is loaded in such a way that it extends it is said to be in tension. On the other hand, if the material compresses and shortens it is said to be in compression.On an atomic level, molecules or atoms are forced together when in compression, whereas they are pulled apart when in tension. Since atoms in solids always try to find an equilibrium position, and distance between other atoms, forces arise throughout the entire material which oppose both tension or compression. The phenomena prevailing on an atomic level are therefore similar.
The "strain" is the relative change in length under applied stress; positive strain characterizes an object under tension load which tends to lengthen it, and a compressive stress that shortens an object gives negative strain. Tension tends to pull small sideways deflections back into alignment, while compression tends to amplify such deflection into buckling.
Compressive strength is measured on materials, components, and structures.
The ultimate compressive strength of a material is the maximum uniaxial compressive stress that it can withstand before complete failure. This value is typically determined through a compressive test conducted using a universal testing machine. During the test, a steadily increasing uniaxial compressive load is applied to the test specimen until it fails. The specimen, often cylindrical in shape, experiences both axial shortening and lateral expansion under the load. As the load increases, the machine records the corresponding deformation, plotting a stress–strain curve that would look similar to the following:
The compressive strength of the material corresponds to the stress at the red point shown on the curve. In a compression test, there is a linear region where the material follows Hooke's law. Hence, for this region, where, this time, refers to the Young's modulus for compression. In this region, the material deforms elastically and returns to its original length when the stress is removed.
This linear region terminates at what is known as the yield point. Above this point the material behaves plastically and will not return to its original length once the load is removed.
There is a difference between the engineering stress and the true stress. By its basic definition the uniaxial stress is given by:
where is load applied and is area .
As stated, the area of the specimen varies on compression. In reality therefore the area is some function of the applied load i.e.. Indeed, stress is defined as the force divided by the area at the start of the experiment. This is known as the engineering stress, and is defined bywhere is the original specimen area .
Correspondingly, the engineering strain is defined bywhere is the current specimen length and is the original specimen length . True strain, also known as logarithmic strain or natural strain, provides a more accurate measure of large deformations, such as in materials like ductile metalsThe compressive strength therefore corresponds to the point on the engineering stress–strain curve defined by
where is the load applied just before crushing and is the specimen length just before crushing.
Deviation of engineering stress from true stress
When a uniaxial compressive load is applied to an object it will become shorter and spread laterally so its original cross sectional area increases to the loaded area. Thus the true stress deviates from engineering stress. Tests that measure the engineering stress at the point of failure in a material are often sufficient for many routine applications, such as quality control in concrete production. However, determining the true stress in materials under compressive loads is important for research focused on the properties on new materials and their processing.The geometry of test specimens and friction can significantly influence the results of compressive stress tests. Friction at the contact points between the testing machine and the specimen can restrict the lateral expansion at its ends leading to non-uniform stress distribution. This is discussed in section on [|contact with friction].
Frictionless contact
With a compressive load on a test specimen it will become shorter and spread laterally so its cross sectional area increases and the true compressive stress isand the engineering stress isThe cross sectional area and consequently the stress are uniform along the length of the specimen because there are no external lateral constraints. This condition represents an ideal test condition. For all practical purposes the volume of a high bulk modulus material is not changed by uniaxial compression. SoUsing the strain equation from aboveandNote that compressive strain is negative, so the true stress is less than the engineering stress. The true strain can be used in these formulas instead of engineering strain when the deformation is large.Contact with friction
As the load is applied, friction at the interface between the specimen and the test machine restricts the lateral expansion at its ends. This has two effects:- It can cause non-uniform stress distribution across the specimen, with higher stress at the centre and lower stress at the edges, which affects the accuracy of the result.
- It causes a barreling effect in ductile materials. This changes the specimen's geometry and affects its load-bearing capacity, leading to a higher apparent compressive strength.
- Applying a suitable lubricant, such as MoS2, oil or grease; however, care must be taken not to affect the material properties with the lubricant used.
- Use of PTFE or other low-friction sheets between the test machine and specimen.
- A spherical or self-aligning test fixture, which can minimize friction by applying the load more evenly across the specimen's surface.
- [|Correction formulas]
- [|Geometric extrapolation]
- [|Finite element analysis]
Correction formulas
Note that if there is [|frictionless contact] between the ends of the specimen and the test machine, the bulge radius becomes infinite and. In this case, the formulas yield the same result as because changes according to the ratio.
The parameters obtained from a test result can be used with these formulas to calculate the equivalent true stress at failure.
The graph of [|specimen shape effect] shows how the ratio of true stress to engineering stress varies with the aspect ratio of the test specimen. The curves were calculated using the formulas provided above, based on the specific values presented in the table for [|specimen shape effect calculations]. For the curves where end restraint is applied to the specimens, they are assumed to be fully laterally restrained, meaning that the coefficient of friction at the contact points between the specimen and the testing machine is greater than or equal to one. As shown in the graph, as the relative length of the specimen increases, the ratio of true to engineering stress approaches the value corresponding to frictionless contact between the specimen and the machine, which is the ideal test condition.
Geometric extrapolation
As shown in the section on [|correction formulas], as the length of test specimens is increased and their aspect ratio approaches zero, the compressive stresses approach the true value. However, conducting tests with excessively long specimens is impractical, as they would fail by buckling before reaching the material's true compressive strength. To overcome this, a series of tests can be conducted using specimens with varying aspect ratios, and the true compressive strength can then be determined through extrapolation.Finite element analysis
Comparison of compressive and tensile strengths
Concrete and ceramics typically have much higher compressive strengths than tensile strengths. Composite materials, such as glass fiber epoxy matrix composite, tend to have higher tensile strengths than compressive strengths. Metals are difficult to test to failure in tension vs compression. In compression metals fail from buckling/crumbling/45° shear which is much different than tension which fails from defects or necking down.Compressive failure modes
If the ratio of the length to the effective radius of the material loaded in compression 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, 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.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 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. 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.