2010年11月21日 星期日

RE: Stress-strain diagram

 

Stress-strain diagram

Sunday, November 21, 2010

17:20

Description: Machine generated alternative text: Suppose that a metal specimen be placed in tension-compression-testing machina As the axial
load is gradually increased in increments, the total elongation over the gauge length is
measured at each increment of the load and this is continued until failure of the specimen takes
place- Knowing the original cross-sectional area and length of the specimen. the normal stressa
and the strain can be obtained The graph of these quantities with the stressa along the y-axis
and the strain along the x-axis is called the stress-strain diagram The stress-strain diagram
differs in form for various materials- The diagram shown below is that for a medium-carbon
structural steeL
Metallic engineering materials are classified as either ductile or brittle materials- A ductile
material is one having relatively large tensile strains up to the point of rupture like structural steel
and aluminum. whereas brittle materials has a relatively small strain up to the point of rupture like
cast iron and concrete- An arbitrary strain of O-05 mmimm is frequently taken as the dividing line
between these two classes
t
V)
Actual Rupture Strength ??..
U ? Ultimate Strength
L E ? Elac
L P ? Propoftional Limit
Strain, s

R ? Rupture Strength ?
Y ? Yield Point
Stress-strain diagram of a medium-carbon structural steel

Description: Machine generated alternative text: Proportional Limit (Hooke Law)
From the origin O to the point called proportional limit, the stress-
strain curve is a straight lina This linear relation between
elongation and the axial force causing was first noticed by Sir
Robert Hooke in 1678 and is called Hooke Law that within the
proportional limit, the stress is directly proportional to strain or
u ac e or u = ke
The constant of proportionality k is called the Modulus of
Elasticity E or Young Modulus and is equal to the slope of the
stress-strain diagram from O to P. Then
o? = EF
Elastic Limit
The elastic limit is the limit beyond which the material will no longer
go back to its original shape when the load is removed, or it is the maximum stress that may e
developed such that there is no permanent or residual deformation when the load is entirely
removed
Elastic Limit
The elastic limit is the limit beyond which the material will no longer go back to its original shape
when the load is removed, or it is the maximum stress that may e developed such that there is no
permanent or residual deformation when the load is entirely removed
Elastic and Plastic Ranges
The region in stress-strain diagram from O to P is called the elastic range- The region from P to
R is called the plastic range.
Robert Hooke

Description: Machine generated alternative text: Yield Point
Yield point is the point at which the material will have an appreciable elongation or yielding
without any increase in load
Ultimate Strength
The maximum ordinate in the stress-strain diagram is the ultimate strength or tensile strength
Rapture Strength
Rapture strength is the strength of the material at ruptureS This is also known as the breaking
strength
Modulus of Resilience
Modulus of resilience is the work done on a unit volume of material as the force is gradually
increased from Oto P. in Nm/m3 This may be calculated as the area under the stress-strain
curve from the origin O to up to the elastic limit E (the shaded area in the flgure) The resilience
of the material is its ability to absorb energy without creating a permanent distortion.
Modulus of Toughness
Modulus of toughness is the work done on a unit volume of material as the force is gradually
increased from O to R. in N-m1m3 This may be calculated as the area under the entire stress
strain curve (from O to R). The toughness of a material is its ability to absorb energy without
causing it to breat

Description: Machine generated alternative text: Working Stress, Allowable Stress, and Factor of Safety
Working stress is defined as the actual stress of a material under a given loading The maximum
safe stress that a material can carry is termed as the allowable stress. The allowable stress
should be limited to values not exceeding the proportional limit. However, since proportional limit
is difficult to determine accurately. the allowable tress is taken as either the yield point or ultimate
strength divided by a factor of safety. The ratio of this strength (ultimate or yield strength) to
allowable strength is called the factor of safety.

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