Similitud de ideales
5.2 Clases de ideales
High temperature failures is a significant problem. A failure analysis can identify the root cause of your failure to prevent reoccurrence. AMC can provide failure analysis of high temperature failures to identify the root cause of your component failure.
3.13 STRESS
Stress is defined as force per unit area. It has the same units as pressure, and in fact pressure is one special variety of stress. However, stress is a much more complex quantity than pressure because it varies both with direction and with the surface it acts on.
Stress = Load / cross-sectional area ( N / mm2)
• Compression:
Stress that acts to shorten an object.
• Tension:
Stress that acts to lengthen an object.
• Normal Stress:
Stress that acts perpendicular to a surface. Can be either compressional or tensional.
• Shear:
Stress that acts parallel to a surface. It can cause one object to slide over another. It also tends to deform originally rectangular objects into parallelograms. The most general definition is that shear acts to change the angles in an object.
• Hydrostatic:
Stress (usually compressional) that is uniform in all directions. A scuba diver experiences hydrostatic stress. Stress in the earth is nearly hydrostatic. The term for uniform stress in the earth is lithostatic.
• Directed Stress:
Stress that varies with direction. Stress under a stone slab is directed; there is a force in one direction but no counteracting forces perpendicular to it. This is why a person under a thick slab gets squashed but a scuba diver under the same pressure doesn't. The scuba diver feels the same force in all directions.
3.14 STRAIN
You will also be able to find the amount of stretch or elongation the specimen undergoes during tensile testing This can be expressed as an absolute measurement in the change in length or as a relative measurement called "strain". Strain itself can be expressed in two different ways, as "engineering strain"
and "true strain". Engineering strain is probably the easiest and the most common expression of strain used. It is the ratio of the change in length to the original length,
. Whereas, the true strain is similar but based on the instantaneous length of the specimen as the test progresses,
, where Li is the instantaneous length and L0 the initial length.
• Longitudinal or Linear Strain
Strain that changes the length of a line without changing its direction. Can be either compressional or tensional.
• Compression
Longitudinal strain that shortens an object.
• Tension
Longitudinal strain that lengthens an object.
• Shear
Strain that changes the angles of an object. Shear causes lines to rotate.
• Infinitesimal Strain:
Strain that is tiny, a few percent or less. Allows a number of useful mathematical simplifications and approximations.
• Finite Strain:
Strain larger than a few percent. Requires a more complicated mathematical treatment than infinitesimal strain.
• Homogeneous Strain:
Uniform strain. Straight lines in the original object remain straight. Parallel lines remain parallel.
Circles deform to ellipses. Note that this definition rules out folding, since an originally straight layer has to remain straight.
• Inhomogeneous Strain:
How real geology behaves. Deformation varies from place to place. Lines may bend and do not necessarily remain parallel.
3.15 Terms for behavior of materials
• Elastic:
Material deforms under stress but returns to its original size and shape when the stress is released.
There is no permanent deformation. Some elastic strain, like in a rubber band, can be large, but in rocks it is usually small enough to be considered infinitesimal.
• Brittle:
Material deforms by fracturing. Glass is brittle. Rocks are typically brittle at low temperatures and pressures.
• Ductile:
Material deforms without breaking. Metals are ductile. Many materials show both types of behavior. They may deform in a ductile manner if deformed slowly, but fracture if deformed too quickly or too much. Rocks are typically ductile at high temperatures or pressures.
• Viscous:
Materials that deform steadily under stress. Purely viscous materials like liquids deform under even the smallest stress. Rocks may behave like viscous materials under high temperature and pressure.
• Plastic:
Material does not flow until a threshhold stress has been exceeded.
• Viscoelastic:
Combines elastic and viscous behavior. Models of glacio-isostasy frequently assume a viscoelastic earth: the crust flexes elastically and the underlying mantle flows viscously.
3.16 Strain-Stress Diagram
A stress-strain curve is a graph derived from measuring load (stress - σ) versus extension (strain - ε) for a sample of a material. The nature of the curve varies from material to material. The following diagrams illustrate the stress-strain behaviour of typical materials in terms of the engineering stress and engineering strain where the stress and strain are calculated based on the original dimensions of the sample and not the instantaneous values. In each case the samples are loaded in tension although in many cases similar behaviour is observed in compression.
The stress value at the point P is called the limit of proportionality:
σ = F / Sp P 0
This behavior conforms to the Hook’s Law:
σ = E*δ
Where E is a constant, known as Young’s Modulus or Modulus of Elasticity.
The value of Young’s Modulus is determined mainly by the nature of the material and is nearly insensitive to the heat treatment and composition.
Modulus of elasticity determines stiffness - resistance of a body to elastic deformation caused by an applied force.
The line 0E in the strain-stress curve indicates the range of elastic deformation – removal of the load at any point of this part of the curve results in return of the specimen length to its original value.
The elastic behavior is characterized by the elasticity limit (stress value at the point E):
σ = F / Sel E 0
For the most materials the points P and E coincide and therefore σ =σel p.
A point where the stress causes sudden deformation without any increase in the force is called yield limit (yield stress, yield strength):
σ = F / Sy Y 0
The highest stress (point YU) , occurring before the sudden deformation is called upper yield limit . The lower stress value, causing the sudden deformation (point YL) is called lower yield limit.
The commonly used parameter of yield limit is actually lower yield limit.
If the load reaches the yield point the specimen undergoes plastic deformation – it does not return to its original length after removal of the load.
Hard steels and non-ferrous metals do not have defined yield limit, therefore a stress, corresponding to a definite deformation (0.1% or 0.2%) is commonly used instead of yield limit. This stress is called proof stress or offset yield limit (offset yield strength):
σ0.2%= F0.2% / S0
The method of obtaining the proof stress is shown in the picture.
As the load increase, the specimen continues to undergo plastic deformation and at a certain stress value its cross-section decreases due to “necking” (point S in the strain-stress diagram). At this point the stress reaches the maximum value, which is called ultimate tensile strength (tensile strength):
σ = F / St S 0
Continuation of the deformation results in breaking the specimen - the point B in the diagram.
The actual strain-stress curve is obtained by taking into account the true specimen cross-section instead of the original value.
Other important characteristic of metals is ductility - ability of a material to deform under tension without rupture.
Two ductility parameters may be obtain from the tensile test:
Relative elongation - ratio between the increase of the specimen length before its rupture and its original length:
δ = (L – L ) / Lm 0 0
Where Lm– maximum specimen length.
Relative reduction of area - ratio between the decrease of the specimen cross-section area before its rupture and its original cross-section area:
ψ= (S – S ) / S0 min 0
Where Smin– minimum specimen cross-section area.
3.17 HOOKE,S LAW
For most tensile testing of materials, you will notice that in the initial portion of the test, the relationship between the applied force, or load, and the elongation the specimen exhibits is linear. In this linear region, the line obeys the relationship defined as "Hooke's Law" where the ratio of stress to strain is a constant, or . E is the slope of the line in this region where stress (σ) is proportional to strain (ε) and is called the
"Modulus of Elasticity" or "Young's Modulus".