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| [[Rodney Hill]] has developed several yield criteria for anisotropic plastic deformations. The earliest version was a straightforward extension of the [[von Mises yield criterion]] and had a quadratic form. This model was later generalized by allowing for an exponent ''m''. Variations of these criteria are in wide use for metals, polymers, and certain composites.
| |
|
| |
|
| == Quadratic Hill yield criterion ==
| |
| The quadratic Hill yield criterion<ref>R. Hill. (1948). ''A theory of the yielding and plastic flow of anisotropic metals.'' Proc. Roy. Soc. London, 193:281–297</ref> has the form
| |
| :<math>
| |
| F(\sigma_{22}-\sigma_{33})^2 + G(\sigma_{33}-\sigma_{11})^2 + H(\sigma_{11}-\sigma_{22})^2 + 2L\sigma_{23}^2 + 2M\sigma_{31}^2 + 2N\sigma_{12}^2 = 1 ~.
| |
| </math>
| |
| Here ''F, G, H, L, M, N'' are constants that have to be determined experimentally and <math>\sigma_{ij}</math> are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent. It predicts the same yield stress in tension and in compression.
| |
|
| |
|
| === Expressions for F, G, H, L, M, N ===
| | They are typically a free website that are pre-designed for enabling businesses of every size in marking the presence on the internet and allows them in showcasing the product services and range through images, contents and various other elements. This one is one of the most beneficial features of Word - Press as this feature allows users to define the user roles. PSD files are incompatible to browsers and are suppose to be converted into wordpress compatible files so that it opens up in browser. If you need a special plugin for your website , there are thousands of plugins that can be used to meet those needs. The top 4 reasons to use Business Word - Press Themes for a business website are:. <br><br>Any business enterprise that is certainly worth its name should really shell out a good deal in making sure that they have the most effective website that provides related info to its prospect. You do not catch a user's attention through big and large pictures that usually takes a millennium to load up. Well Managed Administration The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. From my very own experiences, I will let you know why you should choose WPZOOM Live journal templates. By using Word - Press, you can develop very rich, user-friendly and full-functional website. <br><br>ve labored so hard to publish and put up on their website. When a business benefits from its own domain name and a tailor-made blog, the odds of ranking higher in the search engines and being visible to a greater number of people is more likely. After age 35, 18% of pregnancies will end in miscarriage. Storing write-ups in advance would have to be neccessary with the auto blogs. If you have any kind of inquiries regarding where and how you can utilize [http://ad4.fr/wordpress_backup_2336051 wordpress backup], you can contact us at our web site. Purchase these from our site, or bring your own, it doesn't matter, we will still give you free installation and configuration. <br><br>It has become a more prevalent cause of infertility and the fertility clinic are having more and more couples with infertility problems. But the Joomla was created as the CMS over years of hard work. Normally, the Word - Press developers make a thorough research on your website goals and then ingrain the most suitable graphical design elements to your website. So, we have to add our social media sharing buttons in website. If your site does well you can get paid professional designer to create a unique Word - Press theme. <br><br>A sitemap is useful for enabling web spiders and also on rare occasions clients, too, to more easily and navigate your website. If you operate a website that's been built on HTML then you might have to witness traffic losses because such a site isn't competent enough in grabbing the attention of potential consumers. Useful Plugins Uber - Menu Top Megamenu Now it is the time of sticky Top navbar. Word - Press is an open source content management system which is easy to use and offers many user friendly features. Article Source: Hostgator discount coupons for your Wordpress site here. |
| If the axes of material anisotropy are assumed to be orthogonal, we can write
| |
| :<math>
| |
| (G + H)~(\sigma_1^y)^2 = 1 ~;~~ (F + H)~(\sigma_2^y)^2 = 1 ~;~~ (F + G)~(\sigma_3^y)^2 = 1
| |
| </math>
| |
| where <math>\sigma_1^y, \sigma_2^y, \sigma_3^y</math> are the normal yield stresses with respect to the axes of anisotropy. Therefore we have
| |
| :<math>
| |
| F = \cfrac{1}{2}\left[\cfrac{1}{(\sigma_2^y)^2} + \cfrac{1}{(\sigma_3^y)^2} - \cfrac{1}{(\sigma_1^y)^2}\right]
| |
| </math>
| |
| :<math>
| |
| G = \cfrac{1}{2}\left[\cfrac{1}{(\sigma_3^y)^2} + \cfrac{1}{(\sigma_1^y)^2} - \cfrac{1}{(\sigma_2^y)^2}\right]
| |
| </math>
| |
| :<math>
| |
| H = \cfrac{1}{2}\left[\cfrac{1}{(\sigma_1^y)^2} + \cfrac{1}{(\sigma_2^y)^2} - \cfrac{1}{(\sigma_3^y)^2}\right]
| |
| </math>
| |
| Similarly, if <math>\tau_{12}^y, \tau_{23}^y, \tau_{31}^y</math> are the yield stresses in shear (with respect to the axes of anisotropy), we have
| |
| :<math>
| |
| L = \cfrac{1}{2~(\tau_{23}^y)^2} ~;~~ M = \cfrac{1}{2~(\tau_{31}^y)^2} ~;~~ N = \cfrac{1}{2~(\tau_{12}^y)^2}
| |
| </math>
| |
| | |
| === Quadratic Hill yield criterion for plane stress ===
| |
| The quadratic Hill yield criterion for thin rolled plates (plane stress conditions) can be expressed as
| |
| :<math>
| |
| \sigma_1^2 + \cfrac{R_0~(1+R_{90})}{R_{90}~(1+R_0)}~\sigma_2^2 - \cfrac{2~R_0}{1+R_0}~\sigma_1\sigma_2 = (\sigma_1^y)^2
| |
| </math>
| |
| where the principal stresses <math>\sigma_1, \sigma_2</math> are assumed to be aligned with the axes of anisotropy with <math>\sigma_1</math> in the rolling direction and <math>\sigma_2</math> perpendicular to the rolling direction, <math>\sigma_3 = 0 </math>, <math>R_0</math> is the [[Lankford coefficient|R-value]] in the rolling direction, and <math>R_{90}</math> is the [[Lankford coefficient|R-value]] perpendicular to the rolling direction.
| |
| | |
| For the special case of transverse isotropy we have <math>R=R_0 = R_{90}</math> and we get
| |
| :<math>
| |
| \sigma_1^2 + \sigma_2^2 - \cfrac{2~R}{1+R}~\sigma_1\sigma_2 = (\sigma_1^y)^2
| |
| </math>
| |
| | |
| :{| class="toccolours jy
| |
| collapsible collapsed "width="80%" style="text-align:left"
| |
| !Derivation of Hill's criterion for plane stress
| |
| |-
| |
| | For the situation where the principal stresses are aligned with the directions of anisotropy we have
| |
| :<math> | |
| f := F(\sigma_2-\sigma_3)^2 + G(\sigma_3-\sigma_1)^2 + H(\sigma_1-\sigma_2)^2 - 1 = 0 \,
| |
| </math>
| |
| where <math>\sigma_1, \sigma_2, \sigma_3</math> are the principal stresses. If we assume an associated flow rule we have
| |
| :<math>
| |
| \epsilon^p_i = \lambda~\cfrac{\partial f}{\partial \sigma_i} \qquad \implies \qquad
| |
| \cfrac{d\epsilon^p_i}{d\lambda} = \cfrac{\partial f}{\partial \sigma_i} ~.
| |
| </math>
| |
| This implies that
| |
| :<math>
| |
| \begin{align}
| |
| \cfrac{d\epsilon^p_1}{d\lambda} &= 2(G+H)\sigma_1 - 2H\sigma_2 - 2G\sigma_3 \\
| |
| \cfrac{d\epsilon^p_2}{d\lambda} &= 2(F+H)\sigma_2 - 2H\sigma_1 - 2F\sigma_3 \\
| |
| \cfrac{d\epsilon^p_3}{d\lambda} &= 2(F+G)\sigma_3 - 2G\sigma_1 - 2F\sigma_2 ~.
| |
| \end{align}
| |
| </math>
| |
| For plane stress <math>\sigma_3 = 0</math>, which gives
| |
| :<math>
| |
| \begin{align}
| |
| \cfrac{d\epsilon^p_1}{d\lambda} &= 2(G+H)\sigma_1 - 2H\sigma_2\\
| |
| \cfrac{d\epsilon^p_2}{d\lambda} &= 2(F+H)\sigma_2 - 2H\sigma_1\\
| |
| \cfrac{d\epsilon^p_3}{d\lambda} &= - 2G\sigma_1 - 2F\sigma_2 ~.
| |
| \end{align}
| |
| </math>
| |
| The [[Lankford coefficient|R-value]] <math>R_0</math> is defined as the ratio of the in-plane and out-of-plane plastic strains under uniaxial stress <math>\sigma_1</math>. The quantity <math>R_{90}</math> is the plastic strain ratio under uniaxial stress <math>\sigma_2</math>. Therefore, we have
| |
| :<math>
| |
| R_0 = \cfrac{d\epsilon^p_2}{d\epsilon^p_3} = \cfrac{H}{G} ~;~~
| |
| R_{90} = \cfrac{d\epsilon^p_1}{d\epsilon^p_3} = \cfrac{H}{F} ~.
| |
| </math>
| |
| Then, using <math>H=R_0 G</math> and <math>\sigma_3=0</math>, the yield condition can be written as
| |
| :<math>
| |
| f := F \sigma_2^2 + G \sigma_1^2 + R_0 G(\sigma_1-\sigma_2)^2 - 1 = 0 \,
| |
| </math>
| |
| which in turn may be expressed as
| |
| :<math>
| |
| \sigma_1^2 + \cfrac{F+R_0 G}{G(1+R_0)}~\sigma_2^2 - \cfrac{2R_0}{1+R_0}~\sigma_1\sigma_2 = \cfrac{1}{(1+R_0)G}~.
| |
| </math>
| |
| This is of the same form as the required expression. All we have to do is to express <math>F,G</math> in terms of <math>\sigma_1^y</math>. Recall that,
| |
| :<math>
| |
| \begin{align}
| |
| F & = \cfrac{1}{2}\left[\cfrac{1}{(\sigma_2^y)^2} + \cfrac{1}{(\sigma_3^y)^2} - \cfrac{1}{(\sigma_1^y)^2}
| |
| \right] \\
| |
| G & = \cfrac{1}{2}\left[\cfrac{1}{(\sigma_3^y)^2} + \cfrac{1}{(\sigma_1^y)^2} - \cfrac{1}{(\sigma_2^y)^2}
| |
| \right] \\
| |
| H & = \cfrac{1}{2}\left[\cfrac{1}{(\sigma_1^y)^2} + \cfrac{1}{(\sigma_2^y)^2} - \cfrac{1}{(\sigma_3^y)^2}
| |
| \right]
| |
| \end{align}
| |
| </math>
| |
| We can use these to obtain
| |
| :<math>
| |
| \begin{align}
| |
| R_0 = \cfrac{H}{G} & \implies
| |
| (1+R_0)\cfrac{1}{(\sigma_3^y)^2} - (1+R_0)\cfrac{1}{(\sigma_2^y)^2} = (1-R_0)\cfrac{1}{(\sigma_1^y)^2} \\
| |
| R_{90} = \cfrac{H}{F} & \implies
| |
| (1+R_{90})\cfrac{1}{(\sigma_3^y)^2} - (1-R_{90})\cfrac{1}{(\sigma_2^y)^2} = (1+R_{90})\cfrac{1}{(\sigma_1^y)^2}
| |
| \end{align}
| |
| </math>
| |
| Solving for <math>\cfrac{1}{(\sigma_3^y)^2}, \cfrac{1}{(\sigma_2^y)^2}</math> gives us
| |
| :<math>
| |
| \cfrac{1}{(\sigma_3^y)^2} = \cfrac{R_0+R_{90}}{(1+R_0)~R_{90}}~\cfrac{1}{(\sigma_1^y)^2} ~;~~
| |
| \cfrac{1}{(\sigma_2^y)^2} = \cfrac{R_0(1+R_{90})}{(1+R_0)~R_{90}}~\cfrac{1}{(\sigma_1^y)^2}
| |
| </math>
| |
| Plugging back into the expressions for <math>F,G</math> leads to
| |
| :<math>
| |
| F = \cfrac{R_0}{(1+R_0)~R_{90}}~\cfrac{1}{(\sigma_1^y)^2} ~;~~
| |
| G = \cfrac{1}{1+R_0}~\cfrac{1}{(\sigma_1^y)^2}
| |
| </math>
| |
| which implies that
| |
| :<math>
| |
| \cfrac{1}{G(1+R_0)} = (\sigma_1^y)^2 ~;~~ \cfrac{F+R_0 G}{G(1+R_0)} = \cfrac{R_0(1+R_{90})}{R_{90}(1+R_0)} ~.
| |
| </math>
| |
| Therefore the plane stress form of the quadratic Hill yield criterion can be expressed as
| |
| :<math>
| |
| \sigma_1^2 + \cfrac{R_0~(1+R_{90})}{R_{90}~(1+R_0)}~\sigma_2^2 - \cfrac{2~R_0}{1+R_0}~\sigma_1\sigma_2 = (\sigma_1^y)^2
| |
| </math>
| |
| |}
| |
| | |
| == Generalized Hill yield criterion ==
| |
| The generalized Hill yield criterion<ref>R. Hill. (1979). '' Theoretical plasticity of textured aggregates. '' Math. Proc. Camb. Phil. Soc., 85(1):179–191.</ref> has the form
| |
| :<math>
| |
| \begin{align}
| |
| F|\sigma_{2}-\sigma_{3}|^m & + G|\sigma_{3}-\sigma_{1}|^m + H|\sigma_{1}-\sigma_{2}|^m + L|2\sigma_1 - \sigma_2 - \sigma_3|^m \\
| |
| & + M|2\sigma_2 - \sigma_3 - \sigma_1|^m + N|2\sigma_3 - \sigma_1 - \sigma_2|^m = \sigma_y^m ~.
| |
| \end{align}
| |
| </math>
| |
| where <math>\sigma_i</math> are the principal stresses (which are aligned with the directions of anisotropy), <math>\sigma_y</math> is the yield stress, and ''F, G, H, L, M, N'' are constants. The value of ''m'' is determined by the degree of anisotropy of the material and must be greater than 1 to ensure convexity of the yield surface.
| |
| | |
| === Generalized Hill yield criterion for plane stress ===
| |
| For transversely isotropic materials with <math>1-2</math> being the plane of symmetry, the generalized Hill yield criterion reduces to (with <math>F=G</math> and <math>L=M</math>)
| |
| :<math>
| |
| \begin{align}
| |
| f := & F|\sigma_2-\sigma_3|^m + F|\sigma_3-\sigma_1|^m + H|\sigma_1-\sigma_2|^m + L|2\sigma_1 - \sigma_2 - \sigma_3|^m \\
| |
| & + L|2\sigma_2-\sigma_3-\sigma_1|^m + N|2\sigma_3-\sigma_1-\sigma_2|^m - \sigma_y^m \le 0
| |
| \end{align}
| |
| </math>
| |
| The [[R-value (plasticity)|R-value]] or [[Lankford coefficient]] can be determined by considering the situation where <math>\sigma_1 > (\sigma_2 = \sigma_3 = 0)</math>. The R-value is then given by
| |
| :<math>
| |
| R = \cfrac{(2^{m-1}+2) L - N + H}{(2^{m-1} - 1) L + 2 N + F} ~.
| |
| </math>
| |
| Under [[plane stress]] conditions and with some assumptions, the generalized Hill criterion can take several forms.<ref>Chu, E. (1995). ''Generalization of Hill's 1979 anisotropic yield criteria''. Journal of Materials Processing Technology, vol. 50, pp. 207-215.</ref>
| |
| * '''Case 1:''' <math>L = 0, H = 0.</math>
| |
| :<math>
| |
| f:= \cfrac{1+2R}{1+R}(|\sigma_1|^m + |\sigma_2|^m) - \cfrac{R}{1+R} |\sigma_1 + \sigma_2|^m - \sigma_y^m \le 0
| |
| </math>
| |
| * '''Case 2:''' <math>N = 0, F = 0.</math>
| |
| :<math>
| |
| f:= \cfrac{2^{m-1}(1-R)+(R+2)}{(1-2^{m-1})(1+R)}|\sigma_1 -\sigma_2|^m - \cfrac{1}{(1-2^{m-1})(1+R)} (|2\sigma_1 - \sigma_2|^m + |2\sigma_2-\sigma_1|^m)- \sigma_y^m \le 0
| |
| </math>
| |
| * '''Case 3:''' <math>N = 0, H = 0.</math>
| |
| :<math>
| |
| f:= \cfrac{2^{m-1}(1-R)+(R+2)}{(2+2^{m-1})(1+R)}(|\sigma_1|^m -|\sigma_2|^m) + \cfrac{R}{(2+2^{m-1})(1+R)} (|2\sigma_1 - \sigma_2|^m + |2\sigma_2-\sigma_1|^m)- \sigma_y^m \le 0
| |
| </math>
| |
| * '''Case 4:''' <math>L = 0, F = 0.</math>
| |
| :<math>
| |
| f:= \cfrac{1+2R}{2(1+R)}|\sigma_1 - \sigma_2|^m + \cfrac{1}{2(1+R)} |\sigma_1 + \sigma_2|^m - \sigma_y^m \le 0
| |
| </math>
| |
| * '''Case 5:''' <math>L = 0, N = 0.</math>. This is the [[Hosford yield criterion]].
| |
| :<math>
| |
| f := \cfrac{1}{1+R}(|\sigma_1|^m + |\sigma_2|^m) + \cfrac{R}{1+R}|\sigma_1-\sigma_2|^m - \sigma_y^m \le 0
| |
| </math>
| |
| : ''Care must be exercised in using these forms of the generalized Hill yield criterion because the yield surfaces become concave (sometimes even unbounded) for certain combinations of'' <math>R</math> and <math>m</math>.<ref>Zhu, Y., Dodd, B., Caddell, R. M. and Hosford, W. F. (1987). ''Limitations of Hill's 1979 anisotropic yield criterion.'' International Journal of Mechanical Sciences, vol. 29, pp. 733.</ref>
| |
| | |
| == Hill 1993 yield criterion ==
| |
| In 1993, Hill proposed another yield criterion <ref>Hill. R. (1993). ''User-friendly theory of orthotropic plasticity in sheet metals.'' International Journal of Mechanical Sciences, vol. 35, no. 1, pp. 19–25.</ref> for plane stress problems with planar anisotropy. The Hill93 criterion has the form
| |
| :<math>
| |
| \left(\cfrac{\sigma_6}{\sigma_0}\right)^2 + \left(\cfrac{\sigma_2}{\sigma_{90}}\right)^2 + \left[ (p + q - c) - \cfrac{p\sigma_1+q\sigma_2}{\sigma_b}\right]\left(\cfrac{\sigma_1\sigma_2}{\sigma_0\sigma_{90}}\right) = 1
| |
| </math>
| |
| where <math>\sigma_0</math> is the uniaxial tensile yield stress in the rolling direction, <math>\sigma_{90}</math> is the uniaxial tensile yield stress in the direction normal to the rolling direction, <math>\sigma_b</math> is the yield stress under uniform biaxial tension, and <math>c, p, q</math> are parameters defined as
| |
| :<math>
| |
| \begin{align}
| |
| c & = \cfrac{\sigma_0}{\sigma_{90}} + \cfrac{\sigma_{90}}{\sigma_0} - \cfrac{\sigma_0\sigma_{90}}{\sigma_b^2} \\
| |
| \left(\cfrac{1}{\sigma_0}+\cfrac{1}{\sigma_{90}}-\cfrac{1}{\sigma_b}\right)~p & =
| |
| \cfrac{2 R_0 (\sigma_b-\sigma_{90})}{(1+R_0)\sigma_0^2} - \cfrac{2 R_{90} \sigma_b}{(1+R_{90})\sigma_{90}^2} + \cfrac{c}{\sigma_0} \\
| |
| \left(\cfrac{1}{\sigma_0}+\cfrac{1}{\sigma_{90}}-\cfrac{1}{\sigma_b}\right)~q & =
| |
| \cfrac{2 R_{90} (\sigma_b-\sigma_{0})}{(1+R_{90})\sigma_{90}^2} - \cfrac{2 R_{0} \sigma_b}{(1+R_{0})\sigma_{0}^2} + \cfrac{c}{\sigma_{90}}
| |
| \end{align}
| |
| </math>
| |
| and <math>R_0</math> is the R-value for uniaxial tension in the rolling direction, and <math>R_{90}</math> is the R-value for uniaxial tension in the in-plane direction perpendicular to the rolling direction.
| |
| | |
| == Extensions of Hill's yield criteria ==
| |
| The original versions of Hill's yield criteria were designed for material that did not have pressure-dependent yield surfaces which are needed to model [[polymer]]s and [[foam]]s.
| |
| | |
| === The Caddell-Raghava-Atkins yield criterion ===
| |
| An extension that allows for pressure dependence is Caddell-Raghava-Atkins (CRA) model <ref>Caddell, R. M., Raghava, R. S. and Atkins, A. G., (1973), ''Yield criterion for anisotropic and pressure dependent solids such as oriented polymers.'' Journal of Materials Science, vol. 8, no. 11, pp. 1641-1646.</ref> which has the form
| |
| :<math>
| |
| F (\sigma_{22}-\sigma_{33})^2 + G (\sigma_{33}-\sigma_{11})^2 + H (\sigma_{11}-\sigma_{22})^2 + 2 L \sigma_{23}^2 + 2 M \sigma_{31}^2 + 2 N\sigma_{12}^2 + I \sigma_{11} + J \sigma_{22} + K \sigma_{33} = 1~.
| |
| </math>
| |
| | |
| === The Deshpande-Fleck-Ashby yield criterion ===
| |
| Another pressure-dependent extension of Hill's quadratic yield criterion which has a form similar to the [[Bresler Pister yield criterion]] is the Deshpande, Fleck and Ashby (DFA) yield criterion <ref>Deshpande, V. S., Fleck, N. A. and [[M. F. Ashby|Ashby, M. F.]] (2001). '' Effective properties of the octet-truss lattice material.'' Journal of the Mechanics and Physics of Solids, vol. 49, no. 8, pp. 1747-1769.</ref> for [[honeycomb structures]] (used in [[Sandwich structured composite|sandwich composite]] construction). This yield criterion has the form
| |
| :<math> | |
| F (\sigma_{22}-\sigma_{33})^2 + G (\sigma_{33}-\sigma_{11})^2 + H (\sigma_{11}-\sigma_{22})^2 + 2 L \sigma_{23}^2 + 2 M \sigma_{31}^2 + 2 N\sigma_{12}^2 + K (\sigma_{11} + \sigma_{22} + \sigma_{33})^2 = 1~.
| |
| </math> | |
| | |
| == References ==
| |
| <references/>
| |
| | |
| == External links ==
| |
| * [http://aluminium.matter.org.uk/content/html/eng/default.asp?catid=183&pageid=2144416653 Yield criteria for aluminum]
| |
| * [http://www.tecnun.es/Asignaturas/estcompmec/documentos/thinsheets.pdf Yield criteria for thin metal sheets]
| |
| | |
| {{DEFAULTSORT:Hill Yield Criteria}}
| |
| [[Category:Plasticity]]
| |
| [[Category:Solid mechanics]]
| |
| [[Category:Yield criteria]]
| |
They are typically a free website that are pre-designed for enabling businesses of every size in marking the presence on the internet and allows them in showcasing the product services and range through images, contents and various other elements. This one is one of the most beneficial features of Word - Press as this feature allows users to define the user roles. PSD files are incompatible to browsers and are suppose to be converted into wordpress compatible files so that it opens up in browser. If you need a special plugin for your website , there are thousands of plugins that can be used to meet those needs. The top 4 reasons to use Business Word - Press Themes for a business website are:.
Any business enterprise that is certainly worth its name should really shell out a good deal in making sure that they have the most effective website that provides related info to its prospect. You do not catch a user's attention through big and large pictures that usually takes a millennium to load up. Well Managed Administration The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. From my very own experiences, I will let you know why you should choose WPZOOM Live journal templates. By using Word - Press, you can develop very rich, user-friendly and full-functional website.
ve labored so hard to publish and put up on their website. When a business benefits from its own domain name and a tailor-made blog, the odds of ranking higher in the search engines and being visible to a greater number of people is more likely. After age 35, 18% of pregnancies will end in miscarriage. Storing write-ups in advance would have to be neccessary with the auto blogs. If you have any kind of inquiries regarding where and how you can utilize wordpress backup, you can contact us at our web site. Purchase these from our site, or bring your own, it doesn't matter, we will still give you free installation and configuration.
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