|
|
| Line 1: |
Line 1: |
| :''CRSS redirects here. For the Pakistan-based think tank, see [[Center for Research and Security Studies]].''
| | The writer is known as Wilber Pegues. Since I was eighteen I've been working as a bookkeeper but quickly my wife and I will start our own company. The favorite pastime for him and his kids is style and he'll be beginning something else alongside with it. I've usually cherished living in Mississippi.<br><br>my homepage; psychic phone readings - [http://breenq.com/index.php?do=/profile-1144/info/ Highly recommended Internet site], |
| | |
| '''Critical resolved shear stress''' is the component of [[shear stress]], resolved in the direction of slip, necessary to initiate slip in a grain. It is a constant for a given [[crystal]].
| |
| | |
| Tests have been conducted on single crystals of metals to measure the shear stress required to initiate [[plastic deformation]], or cause atomic planes to slip. Since this is a threshold value, it is referred to as critical; and since it is a component of the applied force or stress, it is said to be resolved; that is, the ''critical resolved shear stress.''
| |
| | |
| Resolved shear stress is given by
| |
| τ = σ cos Φ cos λ<ref>Gottstein G., Physical Foundations of Materials Science, Springer, 2004, page 227.</ref>
| |
| where
| |
| σ is the magnitude of the applied tensile stress,
| |
| Φ is the angle between the normal of the slip plane and the direction of the applied force and λ is the angle between the slip plane direction and the direction of the applied force.
| |
| whereas, critical resolved shear stress value is given by
| |
| τ =σ (cosΦ cosλ)max
| |
| | |
| ==Difference between RSS & CRSS==
| |
| | |
| Resolved shear stress is the shear component of an applied tensile (or
| |
| compressive) stress resolved along a slip plane that is other than perpendicular or parallel to the
| |
| stress axis. The critical resolved shear stress is the value of resolved shear stress at which
| |
| yielding begins; it is a property of the material.
| |
| | |
| == Resolved Shear Stress in Crystalline Metals ==
| |
| In metals, slip occurs in specific directions on crystallographic planes. Stress projection factors are used to calculate the stresses on these planes. The most common stress projection factor is the ''Schmid factor'' <ref>Schmid E., Boas W., Plasticity of Crystals with Special Reference to Metals, F.A. Hughes & Co. Ltd., 1935.</ref> which is the maximum value of the term (cosΦ cosλ) for all possible slip planes. The Schmid factor is most applicable to face centered cubic (FCC) single crystal metals.<ref>Hosford W.F., Mechanical Behavior of Materials, 2nd ed., Cambridge University Press, 2010, page 113.</ref>
| |
| | |
| For an FCC system, the Schmid factor for an applied tensile load in the [1 2 3] can be calculated by:
| |
| | |
| :<math> | |
| \begin{align}
| |
| M_{[\text{1 0 1}](\overline{1} 1 1)}=&\frac{(-1*1)+(1*2)+(1*3)}{((-1)^2+1^2+1^2)^{1/2}(1^2+2^2+3^2)^{1/2}}*\frac{(1*1)+(0*2)+(1*3)}{(1^2+0^2+1^2)^{1/2}(1^2+2^2+3^2)^{1/2}}=&\frac{16}{14\sqrt{6}}
| |
| \end{align}</math>
| |
| | |
| The values of slip systems to test using the Schmid Factor are from the <nowiki>{1 1 1}<1 -1 0></nowiki> system. There are 12 different possible parings of the planes and directions. The maximum Schmid factor will indicate the operational slip system(s).<ref>Meyers and Chawla. (1999) ''Mechanical Behaviors of Materials.'' Prentice Hall, Inc. Page 301.</ref>
| |
| | |
| For polycrystal metals, the [[Charles Taylor (physicist)|Taylor]] factor has been shown to be more accurate than the Schmid factor for polycrystal specimens.<ref name="Taylor">Taylor, Sir Geoffrey Ingram. Plastic strain in metals. 1938.</ref> Taylor showed <ref name="Taylor" /> that a minimum of five active slip systems are required to accommodate an arbitrary deformation. The five (or more) active systems are those that, combined, provide the greatest amount of work of deformation.
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| [[Category:Metallurgy]]
| |
| [[Category:Continuum mechanics]]
| |
| [[Category:Deformation]]
| |
The writer is known as Wilber Pegues. Since I was eighteen I've been working as a bookkeeper but quickly my wife and I will start our own company. The favorite pastime for him and his kids is style and he'll be beginning something else alongside with it. I've usually cherished living in Mississippi.
my homepage; psychic phone readings - Highly recommended Internet site,