物理冶金 Homework #3 Due 2019.01.03 PM5

物理冶金 Homework #3 Due 2019.01.03 PM5:00寫奇數題(1) Please explain the relationship the dislocation strain energy and Burgers vector.(2) If a vacancy interacts with a postive egde dislocation, does this vacancy tend to enter the top or bottomof slip plane ? Please give a explaination.(3) If a shear stress (100 N /m2) is applied to a metal crystal that contain a edge dislolcation with a length of100μm and a Burgers vector of[11 0]2ab =, a=0.543nm. Please calcualte the force on this dislocation.(4) 4.14 The strain energy of a dislocation normally varies as the square of its Burgers vector. One maysee this by examining Eqs. 4.19 and 4.20. This relationship between the dislocation strain energy and theBurgers vector is known as Frank’s rule. Thus, if = [ℎ], where a is a numerical factor, then:⁄m ~ 2{ℎ2 + 2 + 2}Show that in an fcc crystal the dissociation of a total dislocation into its two partials is energeticallyfeasible. See Eq. 4.4.(5) 4.16 Consider Eq. 4.19, which gives the strain energy per unit length of a screw dislocation. Assumethat one has a very large square array of long, straight, parallel screw dislocations of alternating signs, sothat the effective outer radius ′ of the stain field of the dislocations may be taken as 12√. With the aidof a computer, determine the strain energy per unit length of a screw dislocation as a function of thedislocation density, , between = 1011 and = 1018m/m3.(G=8.6x1010Pa, b=0.248 nm)(6) Please illustrate the Frank-Read source.(7) 5.1 If the shear vectors, , in Fig. 5.1 were moved from the top and bottom faces of the crystal, andapplied to front and rear surfaces, with the forward vector pointing upwards and the rear one downwards,could any of the Frank-Read dislocation segments move as a result of this shearing stress? Explain.(8) Describe the slip systems in BCC, FCC, and HCP. Explain the reasons why the elongation of 304stainless steel is greater than that of 430 stainless steel. (304 steel : FCC, 430 : BCC) (9) Please illustrate briefly the critical resolved shear stress.(10) 5.12 Identify the dislocation in terms of its Burgers vector (using vector notation) that can cross-slipbetween (111) and(111)of a FCC crystal.(11) What is the double cross-slip mechanism of a dislocation? How could this relat with the slip-bandformation?(12) 5.7 (a) Determine the angle between [123], and [321] in a cubic crystal. Check Appendix A to see ifyour answer is correct. (b) Find a combination of two directions that make an angel of 85.90degress with each other.(13) Consider a metal single crystal oriented such that the normal slip plane and the slip direction are atangles of 41.3 degree and 47.9 degree, respectively, with the tensile axis. If the critical resolved shearstress is 20.7 MPa, will an applied stress of 45 MPa cause the single cystal to yield? If not, what stresswill be necessary.(14) If the critical resolved shear stress for yielding in aluminum is 240kPa, calculate tensile stress requiredto cause yielding when the the tensile axis is [001]. (FCC structure)(15) (a) What is critical resolved shear stress (CRSS) ? (b) What will happen to a rod spcemen when theapplied normal stress is larger than CRSS ?(16) 5.14 (a) The diagram accompanying this problem shows a 111 standard projection of a fcc crystal, inwhich the standard stereographic triangles are outlined. Assuming that point a in the figure representsthe orientation of the tensile stress axis, indicate on a copy of this diagram, the path that the crystal axiswould follow during tensile deformation of the crystal. (b) Give the Miller indices of the final orientationof the stress axis.(17) 5.16 For the case of tensile deformation considered in Prob. 5.14, determine the indices of the primary,conjugate, and cross-slip systems, as well as those for the critical plane.(18) 5.21 A tensile test was made on a tensile specimen, with a cylindrical gage section which had adiameter of 10 mm, and a length of 40 mm. After fracture, the length of the gage section was found to be50 mm, the reduction in area 80 percent, and the load at fracture 1000 N. Compute:(a) The specimen elongation.(b) The engineering fracture stress.(c) The true fracture stress, ignoring the correctyion for triaxiality at the neck.(d) The true strain at the neck.(19) Compare the major difference of deformation behavior in curves a and b shown in figure, and furtherdescribe the possible slip mechanism and characteristics of the three regions in curve b.(20) (A) What is the criterion for necking on an engineerig stress vs. engineering strain curve? (B) What isthe criterion for necking on a true stress vs. true strain curve?(21) Dislocation densities are measured in lines per uint area. A well annealed metal sample will containabout 108dislocation lines per m2 whereas ahevily cold worked sample may contain 1016 lines per m2.What are the average s

結果 (繁體中文) 1:

物理冶金作業＃3由於2019年1月3日PM5：00
寫奇數題
（1）請解釋的關係中的位錯的應變能和伯格斯矢量。
（2）如果用一個正EGDE錯位的空缺相互作用，這是否空置傾向於進入頂部或底部
滑移面的？請給一個交代。
（3）如剪切應力（100牛頓/米2
）被施加到包含具有的長度的邊緣dislolcation金屬晶體
100微米和的伯格斯矢量
[11 0]
2
一個
B =
，A = 0.543nm。請calcualte這個錯位的力。
（4）4.14的位錯的應變能正常變化作為其伯格斯矢量的平方。人們可以
看到這通過檢查公式。4.19和4.20。中的位錯的應變能和之間的這種關係
向量被稱為弗蘭克的規則漢堡包。因此，如果= [ℎ]，其中a是數值因子，則：
/m〜
2
{ℎ
2 +
2 +
2
}
一個總位錯的解離證明在FCC晶體成兩個分音在能量上是
可行的。見公式。4.4。
（5）4.16考慮等式 4.19，這使每一個螺型位錯的單位長度的應變能。假設
一個具有非常大的正方形陣列的長的直鏈，交替的跡象平行螺型位錯，因此
，有效半徑外
的位錯的應變場的“可以被取為1
2√
。與輔助
的計算機的，確定每一個螺型位錯作為的函數的單位長度的應變能
的位錯密度，之間= 1011和=1018米/立方米
。（G = 8.6x1010Pa，B = 0.248納米）
（6）請說明弗蘭克-讀源。
（7）5.1如果剪切載體，在圖5.1分別從頂部和晶體的底面移動，並且
施加到前表面和後表面，與向上指向後部一個向下向前矢量和，
可以在任何的弗蘭克-讀錯段移動，因為這剪切應力的結果？說明。
（8）描述了BCC，FCC，和HCP滑系統。說明理由的304伸長率
不銹鋼比的430不銹鋼大。（304鋼：FCC，430：BCC）
（9）請說明簡要的臨界剪切應力。
（10）5.12確定在其伯格斯矢量而言的錯位（使用矢量表示法），可以交叉滑移
（111）之間，並且
（111）
一個FCC晶體。
（11）什麼是錯的雙交滑移機制是什麼？這怎麼可能RELAT與滑帶
形成的？
（12）5.7（a）確定[123]之間的角度，和在一立方晶體[321]。檢查附錄A，看看
你的答案是正確的。（b）求兩個方向，使85.90的天使的組合
輩分彼此。
（13）考慮定向，使得正常滑移面和滑動方向是在金屬單晶
的分別41.3度和47.9度，角度，與拉伸軸。如果臨界剪切
應力為20.7兆帕，將45兆帕的施加應力導致的單個cystal得到？如果不是，有什麼壓力
是必要的。
（14）如果在鋁得到的臨界剪切應力240kPa，需要計算的拉伸應力
，以使得到當拉伸軸為[001]。（FCC結構）
（15）（一）這是臨界剪切應力（CRSS）？（b）中會發生的桿spcemen什麼當
施加正常應力比CRSS更大？
（16）5.14（a）中伴隨這個問題示出了111標準投影一個FCC晶體，在所述的圖
，其中這個標準立體三角形中概述。假設在圖中該點a表示
的拉伸應力軸的取向，表明在該圖的一個副本，該晶軸的路徑
將所述晶體的拉伸變形過程中跟隨。（b）中得到最終取向的米勒指數
的應力軸的。
（17）5.16對拉伸變形中習題考慮的情況下。5.14，確定初級，的索引
綴合物，和交叉滑系統，以及那些用於關鍵平面。
（18）5.21拉伸試驗，製成的拉伸試樣，用圓筒狀的保徑部，其有一個
直徑為10mm，和40mm的長度。斷裂後，保徑部的長度被認為是
50mm時，在面積80％的減少，並且在斷裂1000 N.計算負載：
（A）將試樣的伸長率。
（b）在工程斷裂應力。
（c）在真斷裂應力，忽略在頸部為三軸的correctyion。
（d）在所述頸部的真應變。
（19）比較的變形行為的主要區別在在圖中所示的曲線a和b，並且進一步
描述在曲線b的三個區域的可能滑動機構和特性。
（20）（A）什麼是頸縮的engineerig應力和工程應變曲線上的準則？（B）是什麼
該準則縮頸一個真實應力與真實應變曲線？
（21）的位錯密度在每UINT區線測量。良好退火的金屬樣品將含有
約108
每平方米位錯線，而ahevily冷加工樣品可以包含每平方米1016線
。
什麼是平均小號

結果 (繁體中文) 2:

必須在樹狀檢視中選擇要替換的檔

結果 (繁體中文) 3:

物理冶金Homework #3 Due 2019.01.03 PM5:00
寫奇數題
（1）Please explain the relationship the dislocation strain energy and Burgers vector.
（2）If a vacancy interacts with a postive egde dislocation，does this vacancy tend to enter the top or bottom
of slip plane？Please give a explaination.
（3）If a shear stress（100 N /m2
）is applied to a metal crystal that contain a edge dislolcation with a length of
100μm and a Burgers vector of
[11 0]
2
a
b =
，a=0.543nm. Please calcualte the force on this dislocation.
（4）4.14 The strain energy of a dislocation normally varies as the square of its Burgers vector. One may
see this by examining Eqs. 4.19 and 4.20. This relationship between the dislocation strain energy and the
Burgers vector is known as Frank’s rule. Thus，if = [ℎ]，where a is a numerical factor，then:
⁄m ~
2
{ℎ
2 +
2 +
2
}
Show that in an fcc crystal the dissociation of a total dislocation into its two partials is energetically
feasible. See Eq. 4.4.
（5）4.16 Consider Eq. 4.19，which gives the strain energy per unit length of a screw dislocation. Assume
that one has a very large square array of long，straight，parallel screw dislocations of alternating signs，so
that the effective outer radius
′of the stain field of the dislocations may be taken as 1
2√
. With the aid
of a computer，determine the strain energy per unit length of a screw dislocation as a function of the
dislocation density，between = 1011 and = 1018m/m3
.（G=8.6x1010Pa，b=0.248 nm）
（6）Please illustrate the Frank-Read source.
（7）5.1 If the shear vectors，in Fig. 5.1 were moved from the top and bottom faces of the crystal，and
applied to front and rear surfaces，with the forward vector pointing upwards and the rear one downwards，
could any of the Frank-Read dislocation segments move as a result of this shearing stress？Explain.
（8）Describe the slip systems in BCC，FCC，and HCP. Explain the reasons why the elongation of 304
stainless steel is greater than that of 430 stainless steel.（304 steel：FCC，430：BCC）
（9）Please illustrate briefly the critical resolved shear stress.
（10）5.12 Identify the dislocation in terms of its Burgers vector（using vector notation）that can cross-slip
between（111）and
（111）
of a FCC crystal.
（11）What is the double cross-slip mechanism of a dislocation？How could this relat with the slip-band
formation？
（12）5.7（a）Determine the angle between [123]，and [321] in a cubic crystal. Check Appendix A to see if
your answer is correct.（b）Find a combination of two directions that make an angel of 85.90
degress with each other.
（13）Consider a metal single crystal oriented such that the normal slip plane and the slip direction are at
angles of 41.3 degree and 47.9 degree，respectively，with the tensile axis. If the critical resolved shear
stress is 20.7 MPa，will an applied stress of 45 MPa cause the single cystal to yield？If not，what stress
will be necessary.
（14）If the critical resolved shear stress for yielding in aluminum is 240kPa，calculate tensile stress required
to cause yielding when the the tensile axis is [001].（FCC structure）
（15）（a）What is critical resolved shear stress（CRSS）？（b）What will happen to a rod spcemen when the
applied normal stress is larger than CRSS？
（16）5.14（a）The diagram accompanying this problem shows a 111 standard projection of a fcc crystal，in
which the standard stereographic triangles are outlined. Assuming that point a in the figure represents
the orientation of the tensile stress axis，indicate on a copy of this diagram，the path that the crystal axis
would follow during tensile deformation of the crystal.（b）Give the Miller indices of the final orientation
of the stress axis.
（17）5.16 For the case of tensile deformation considered in Prob. 5.14，determine the indices of the primary，
conjugate，and cross-slip systems，as well as those for the critical plane.
（18）5.21 A tensile test was made on a tensile specimen，with a cylindrical gage section which had a
diameter of 10 mm，and a length of 40 mm. After fracture，the length of the gage section was found to be
50 mm，the reduction in area 80 percent，and the load at fracture 1000 N. Compute:
（a）The specimen elongation.
（b）The engineering fracture stress.
（c）The true fracture stress，ignoring the correctyion for triaxiality at the neck.
（d）The true strain at the neck.
（19）Compare the major difference of deformation behavior in curves a and b shown in figure，and further
describe the possible slip mechanism and characteristics of the three regions in curve b.
（20）（A）What is the criterion for necking on an engineerig stress vs. engineering strain curve？（B）What is
the criterion for necking on a true stress vs. true strain curve？
（21）Dislocation densities are measured in lines per uint area. A well annealed metal sample will contain
about 108
dislocation lines per m2 whereas ahevily cold worked sample may contain 1016 lines per m2
.
What are the average s