From 853d5e76954eaf11a633135012efcdeaa0e6f05a Mon Sep 17 00:00:00 2001 From: Leandro Lucarella Date: Wed, 8 Aug 2007 18:29:08 +0000 Subject: [PATCH] =?utf8?q?Gu=C3=ADas=20de=20Materiales.?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit --- acoplamiento.dia | 570 +++++++++++++++++++++++++++++++++++ guia2/Makefile | 25 ++ guia2/microconstituyente.png | Bin 0 -> 11972 bytes guia2/resolucion_guia2.rst | 415 +++++++++++++++++++++++++ guia2/trabajo-en-frio1.png | Bin 0 -> 34442 bytes guia2/trabajo-en-frio2.png | Bin 0 -> 35826 bytes 6 files changed, 1010 insertions(+) create mode 100644 acoplamiento.dia create mode 100644 guia2/Makefile create mode 100644 guia2/microconstituyente.png create mode 100644 guia2/resolucion_guia2.rst create mode 100644 guia2/trabajo-en-frio1.png create mode 100644 guia2/trabajo-en-frio2.png diff --git a/acoplamiento.dia b/acoplamiento.dia new file mode 100644 index 0000000..b59a619 --- /dev/null +++ b/acoplamiento.dia @@ -0,0 +1,570 @@ + + + + + + + + + + + + + #A4# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + #Acoplamiento +Caucho +Elastomérico# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + #Eje de bomba# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + #Eje de motor# + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/guia2/Makefile b/guia2/Makefile new file mode 100644 index 0000000..91de55e --- /dev/null +++ b/guia2/Makefile @@ -0,0 +1,25 @@ + +opts=--section-subtitles --language=es --use-latex-footnotes --use-latex-citations --use-latex-docinfo --use-latex-toc --use-verbatim-when-possible --hyperlink-color=0 + +all: resolucion_guia2.pdf + +resolucion_guia2.latex: resolucion_guia2.rst + @echo 'Creando $@...' + @rst2latex ${opts} $< > $@ + +resolucion_guia2.pdf: resolucion_guia2.latex + @echo 'Creando $@...' + @pdflatex $< > /dev/null + @pdflatex $< > /dev/null + +clean: clean-tmp + @rm -vf *.latex + +clean-tmp: + @rm -vf *.log *.aux *.out + +clean-all: clean + @rm -vf *.pdf + +.PHONY: clean all + diff --git a/guia2/microconstituyente.png b/guia2/microconstituyente.png new file mode 100644 index 0000000000000000000000000000000000000000..2588a64866c2ff421b6325d2ae8516d03d8e658d GIT binary patch literal 11972 zcmZ{KRb16y^d$z}-QC??(jh6`-6h@KAsy1vARyf(aOv(8q+3#HnDhJ3!^}L)1DE(* zzW1D+Yp=DVRg`3q5eN{VprDZDWF8elT(y}U4q7Y&w~Bx%*g}=MFu4&DW>kVdS>A3roOPygL(D7E{JM3m~O!q zCeES&?)nl=VHz7v+X4-3J2|o>N}DbgCk!5axL<_M&V-poN-Ojui8yAW6a^ON8w?JO zT@7lnURY?kSZ3`gYa zh=(ut(eNHK?q?dLAkv9J_pr6|f@RhgNl)+VyG@*1-r>Q1e;4R?nXsofhTamjEGu>t z@r95;iR;h=^+KnyKFYj3_+f%|*wd>0x^!RcU(WjxNoG6dbe5&r+-fElt9EWhSF3h^O#kj^5dwq1$bSn|%I!bm=bUFBGV1C;65jDqmGusr z6X6wi7j)Zy)LBWd2S)~PZlzzZW6@sn$R~^voKt*#qQjE3k7ea6q>jUX{>invo>Hs`v!5FtCFSfDeiZy(g{o8YErVxiwkX24zwsBN zRvOJERcGQEonL>Ne}EM7MQDT|L^F^rR(&=g=tjJ8W5pYcn3Z<^C|DPzjYa$SJ2_Gm z=~x1pRvMJMFn1+N&-V}54t0#;!Y+Ai6gUIygxY%;AM7>0#Vn;nl+Sg(w~+_i|@nU0s6Qy;U85>aQ2WsA&awTcc~JV@^7F?hjc*7FZghbX{;>kh&+jv3{nC`BIBtA1S;IT37#wL`H4JJebB{c% z+T}1bR?<0Sy$U%ae-jQ@g}4$-aUld&tV9>Y4-Bgn!{zcrK1ewws83~C6bdGC*_~Av zv`kQ9d6ur(8`BpunM>N!VTmu|VWzW@z7+7ftHaC?YR(kGyrE3TLV}C+l4TAKH--9i zBlAPx>1B(^Nom>6dRkJZQd^^AG(Wo#XB#sbzHrB zu-;X-b!^3qHFisKssp{5CPOGYyuBAt^3Tmt`Y%z-XqGCn6#d_%z4~y)7e=ld%3=8lL6Yr>4y&>L ztigdvG+@d2Z2Ilv^Vri(dKED_p#lE}k?PsCaYMGC<8)F9cD@iiZhzffyk*?_C<@Aa{(p3nn$yp|wMtvm>6Ojy!6seZF zM*iJ3XM2xSZi!a+*7|5b9nT*+y{ zprYwr7dpa}|D5D6Y^p0!NVuYxqhR6UNSwxO(EO@(4yCfSctyv?#Yu@FEv+B2C!463 z6trNs)!I%N*`XVUXRrzClP8Ay>T?=K5Vik39>l zGEA6{s%|JI1=l9DQq1Jz2=D6yyK=F;WG*mM*0E~K%A~Nb3lFW9XQRICb3lR1Z>%Rn zTUC=S<{s^bY8=PNCZm?~YM4fHj_GRiP`SauOHS;wHH%k39cxQg1#L$el?rjDjJEGK z{8Q{r>p{F|JG`$%nxwuf3r1)bHrxI##1&#IJOPf6z83P2?X>Ceh>M`k?Kr<6g6asz z+&_EIaE@^_=@7rmmSpg*rS=asbYnGUxHv>w(Dc4q>GQ$Y4=hyhiQ#W^zopEh0ufC1wxM$};QMPR|qlHgwyKE{$MV`$Ur??JprLL^1S;L}pqr!#GOl{%Mf}99l19$-g!l}aAtY!McuXnoL|MUTzh$Z%>YuJXf`}(z8r|h@CmEmZ0=mCutG_(%@X*B=1G|7 zNoEDjk1dLEr8qmL%xM*ZfTd1?ng;JmI=2hw*71oeO)>iU*{THG33XD%7mDk(y^YkB z)tdT#lEbEgrZIDxPYkAY<^;JbS9h;prEXW2L(kv++4qdM; 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En general, granos contiguos tienen +direferentes orientaciones critalográficas y, desde luego, un límite +de grano común. Durante la deformación plástica el desplazamiento o +movimiento de las dislocaciones debe ocurrir a través de este límite de +grano común. El límite de grano actúa como una barrera el movimiento +de las dislocaciones por dos razones: + +1. Puesto que los dos granos tienen orientaciones distintas, una + dislocación que pasara a un grano vecino tendría que cambiar la + dirección de su movimiento; esto se hace más difícil a medida que + aumenta la diferencia en orientación. +2. El desorden atómico dentro del límite de grano producirá una + discontinuidad de los planos de deslizamiento de un grano a otro. + +Un material con grano fino (es decir, uno que tiene granos pequeños) +es más duro y resistente que uno que tiene granos gruesos, puesto que +el primero tiene un área total de límite de grano mayor para impedir +el movimiento de las dislocaciones. + +Endurecimiento por disolución sólida. +------------------------------------- +Al alear los metales con átomos de impurezas que forman disoluciones +sólidas sustitucionales o intersticiales se logra un endurecimiento +del material. Los metales muy puros son casi siempre blandos y menos +resistentes que las aleaciones formadas con el mismo metal base. El +aumento de la concentración de los átomos de impurezas producen un +aumento en la resistencia a la tracción y de la dureza. + +Las aleaciones son más resistentes que los metales puros debido a que +los átomos de impurezas en solución producen una deformación de la red +en los átomos vecinos del solvente. Como resultado de las interacciones +de los campos de deformación de la red de las dislocaciones y de estos +átomos de impurezas, el movimiento de las dislocaciones es más difícil. + +Estos átomos de soluto tienden a segregarse alrededor de las +dislocaciones de tal manera que se reduzca la energía de deformación +total, es decir, que para que se elimine parte de la energía almacenada +en la red alrededor de una dislocación. Para que esto ocurra, +una impureza menor que el átomo de solvente se localiza donde la +deformación de tracción anula parte de la deformación de compresión +de la dislocación. + +Endurecimiento por deformación. +------------------------------- +El fenómeno de endurecimiento por deformación (también llamado +*acritud* o *trabajo en frío*) se explica en base a las interacciones +entre los campos de deformación de las dislocaciones. + +La densidad de las dislocaciones en un metal aumentan con la deformación +(trabajo en frío). En concecuencia la distancia media entre dislocaciones +disminuye, las dislocaciones se posicionan mucho más juntas. En promedio, +las interacciones dislocación-dislocación son repulsivas. El resultado +neto es que el movimiento de una dislocación es limitado debido +a la presencia de otras dislocaciones. A medida que la densidad de +dislocaciones aumenta, la resistencia al movimiento de éstas debido a +otras dislocacionesse hace más pronunciada. Así, la tensión necesaria +para deformar un metal aumenta con la acritud. + +El refuerzo por deformación se utiliza a menudo en la práctica para +aumentar las propiedades mecánicas de los metales durante los procesos +de conformación. + +.. 3 + +¿Cuál es el efecto de hacer una huella muy próxima a una huella preexistente? +============================================================================= +Se medirá más dureza que la real, porque el material habrá realizado +trabajo en frío en ese área, por lo que se habrá endurecido por +deformación. + +.. 4 + +Calcular el radio de la segunda probeta después de la deformación. +================================================================== +Dos probetas cilíndricas previamente no deformadas de una aleación +son endurecidas por deformación reduciendo el área de la sección +(manteniendo la forma circular). Para una probeta, los radios iniciales +y deformados son 15mm y 12mm, respectivamente. La segunda probeta, con +un radio inicial de 11mm, una vez deformada debe tener la misma dureza +que la primera probeta. + +Probeta 1: :m:`$15 mm \longrightarrow 12 mm$` + +Probeta 2: :m:`$11 mm \longrightarrow A_d mm$` + +Calculamos el trabajo en frío de la probeta 1: + +.. raw:: latex + + \[ CW = \frac {15 - 12} {15} = 0.2 \] + +Y luego el diámetro inicial de la probeta 2: + +.. raw:: latex + + \[ + 0.2 = CW = \frac {11 - A_d} {11} + \Longrightarrow A_d = 0.2 \cdot 11 + 11 = 13.2 + \] + +Por lo tanto :m:`$A_d = 13.2 mm$`. + +.. Diagramas + +.. image:: trabajo-en-frio1.png + :align: center + :scale: 95 + +.. image:: trabajo-en-frio2.png + :align: center + :scale: 95 + +.. 5 + +¿Cuál era el radio antes de la deformación? +=========================================== +Para una probeta cilíndrica de cobre trabajado en frío que tiene una +ductilidad (% L) de 15%, si su radio después del trabajo en frío +es 6,4mm. + +Observando el diagrama (c), vemos que para el cobre, para 15 %L +corresponde 22 %CW aproximadamente, por lo tanto: + +.. raw:: latex + + \[ + 0.22 = \frac {A_0 - 6.4} {A_0} = 1 - \frac {6.4} {A_0} + \Longrightarrow A_0 = \frac {1 - 0.22} {6.4} = 8.2 + \] + +Por lo tanto :m:`$A_0 = 8.2 mm$`. + +.. 6 + +Determinar si es posible. Justifique su respuesta. +================================================== +Trabajar en frío un latón para producir una dureza Brinell mínima de +150 y al mismo tiempo producir una ductilidad de por lo menos el 20% L. + +Observando el diagrama (c), podemos observar que para 20% L tenemos 25% +CW. En el diagrama (b), por otro lado, podemos ver que para 25% CW tiene +una resistencia a la tracción de 450 MPa aproximadamente. Finalmente, +observando el diagrama (d), vemos que para esa resistencia en el latón, +corresponde 110 HBr aproximadamente. + +Además observamos, en (d), que al aumentar la dureza, aumenta +la resistencia y por lo tanto, observando en (b), aumenta también +el trabajo jen frío. Sin embargo, al aumentar el trabajo en frío, +disminuye la ductilidad, como se observa en (c). + +Por lo tanto, si con 20% L tengo 110 HBr, necesito aumentar la dureza +a 150 HBr, pero por lo visto anteriormente, esto implica disminuir +la ductilidad. Por lo tanto **no** es posible lograr que un latón +trabajado en frío cuya ductilidad sea de al menos 20% L llegue a una +dureza mínima de 150 HBr. + +.. 7 + +Una probeta cilíndrica de acero trabajada en frío tiene una dureza de 240 HBr. +============================================================================== +Supongo un acero AISI 1040. + +Estimar su ductilidad en alargamiento porcentual. +------------------------------------------------- +Como observamos en el diagrama (d), una dureza de 250 HBr para +un acero corresponde a alrededor de 850 MPa de resistencia a la +tracción. Observando (b) podemos determinar que a esa resistencia +corresponde un 22% de trabajo en frío, que a su vez, significa que el +material tiene un alargamiento porcentual (ductilidad) de 15%, como se +observa en (c). + +Determinar su radio después de la deformación. +---------------------------------------------- +Si la probeta permaneciera cilíndrica durante la deformación y su +radio inicial era de 10.2 mm. + +Además sabemos que la probeta tuvo 22% CW, por lo tanto: + +.. raw:: latex + + \[ + 0.22 = \frac {10.2 - A_d} {10.2} + \Longrightarrow A_d = 10.2 - 0.22 \cdot 10.2 = 7.95 + \] + +Por lo tanto, el radio final será de :m:`$A_d = 7.95 mm$` + +.. 8 + +Explique cómo puede conseguir... +================================ +Una barra cilíndrica de latón de diámetro original igual a 10,2mm +va a ser deformada en frío por trefilado; la sección circular se +mantiene durante la deformación. Se requiere un límite elástico +en exceso de 380 MP a y una ductilidad de por lo menos 15%. Además, +el diámetro final debe ser 7,6mm. + +.. raw:: latex + + \[ + A_0 = 10.2 mm \wedge A_d = 7.6 mm + \Longrightarrow CW = \frac {10.2 - 7.6} {10.2} = 0.25 + \] + +Por lo tanto, la barra tiene 25% CW, lo que significa, al observar +el diagrama (c), que tiene una ductilidad de 18% (mayor que el 15% L +requerido) y un límite elástico de 380 MPa, según el diagrama (a), +que también cumple con lo pedido. + +.. 9 + +Una muestra de 7,5Kg de una aleación magnesio-plomo consiste en... +================================================================== +Una muestra de 7,5Kg de una aleación magnesio-plomo consiste en una +fase de disolución sólida que tiene la composición algo inferior al +límite de solubilidad a 300°C. + +.. note:: Este ejercicio no fue resuelto porque no he podido entender el + enunciado y el jueves pasado no hubo clases así que no se pudo + hacer la consulta correspondiente. + +.. 10 + +Dada Una aleación de 80% Sn - 20% Pb a 180°C, determinar fracciones de masas de: +================================================================================ + +Las fases +--------- + +Observando el diagrama de fases Sn-Pb, observamos a simple vista que +:m:`$\alpha \approx 20 \% Sn$` y :m:`$\beta \approx 98 \% Pb$`. + +Los micro constituyentes primario y eutéctico +---------------------------------------------- +El componente primario será :m:`$\beta$`. + +.. raw:: latex + + \[ W_{\beta_{primario}} = \frac {80 - 61} {98 - 61} = 0.52 \] + \[ W_{eutectico} = \frac {98 - 80} {98 - 61} = 0.48 \] + +El eutéctico +------------ + +.. raw:: latex + + \[ W_{\alpha_{eutectico}} = \frac {98 - 80} {98 - 20} = 0.23 \] + \[ W_{\beta_{total}} = \frac {80 - 20} {98 - 20} = 0.77 \] + \[ \Longrightarrow W_{\beta_{eutectico}} + = W_{\beta_{total}} - W_{\beta_{primario}} + = 0.25 \] + +.. 11 + +Calcular las fracciones de masas de la ferrita y de la cementita en la perlita. +=============================================================================== + +.. raw:: latex + + \[ W_{ferrita} = \frac {6.67 - 0.89} {6.67 - 0.025} = 0.87 \] + \[ W_{cementita} = \frac {0.89 - 0.025} {6.67 - 0.025} = 0.13 \] + +Por lo tanto, la perlita se compone de 87% ferrita y 13% cementita. + +.. 12 + +¿Cuál es la diferencia entre fase y constituyente? +================================================== + +Fase + Es la porción homogénea de un sistema que tiene características + físicas y químicas uniformes. + +Microconstituyente + Es un elemento de la microestructura con una estructura + característica e identificable. Por ejemplo, una estructura + eutéctica de una aleación Pb-Sn es un microconstituyente, aunqnue + se trata de una mezcla de dos fases, porque tiene una estructura + laminar distinta, con una relación fija entre las dos fases. + +.. 13 + +¿Cuál es la diferencia entre un acero hipoeutectoide y un acero hipereutectoide? +================================================================================ +El acero hipoeutectoide se compone de **perlita** + **ferrita primaria**, +mientras que el hipereutectoide se compone de **perlita** + **cementita +primaria** + +.. 14 + +¿Cuál es el %C de un acero al C si la fracción de cementita es de 0.10? +======================================================================= + +.. raw:: latex + + \[ + W_{cementita} = \frac {\%C - 0.025} {6.67 - 0.025} + \Longrightarrow \%C = 0.10 \cdot (6.67 - 0.025) + 0.025 + = 0.69 + \] + +Por lo tanto, el acero tiene 0.69% de carbono. + +.. 15 + +Enfriar hasta temperaturas inferiores a 727°C 3.5 Kg de austenita con 0.95% C. +============================================================================== + +¿Cuál es la fase proeutectoide? +------------------------------- +La cementita. + +¿Cuántos kilogramos de ferrita y de cementita se forman? +-------------------------------------------------------- + +.. raw:: latex + + \[ + W_{ferrita} = \frac {6.67 - 0.95} {6.67 - 0.025} = 0.86 + \Longrightarrow ferrita = 3.5 kg \cdot 0.86 = 3 kg + \] + + \[ + W_{cementita} = \frac {0.95 - 0.025} {6.67 - 0.025} = 0.14 + \Longrightarrow cementita = 3.5 kg \cdot 0.14 = 0.5 kg + \] + + +¿Cuántos kilogramos de perlita y de fase proeutectoide se forman? +----------------------------------------------------------------- + +.. raw:: latex + + \[ + W_{perlita} = \frac {6.67 - 0.95} {6.67 - 0.89} = 0.99 + \Longrightarrow perlita = 3.5 kg \cdot 0.99 = 3.46 kg + \] + + \[ + W_{cementita_{proeutectoide}} = \frac {0.95 - 0.89} {6.67 - 0.89} = 0.01 + \Longrightarrow cementita proeutectoide = 3.5 kg \cdot 0.01 = 0.04 kg + \] + +Esquematizar y designar la micro estructura resultante. +------------------------------------------------------- + +.. image:: microconstituyente.png + :align: center + +.. 16 + +Enfriar hasta temperaturas inferiores a 727°C, 6 Kg. de austenita con 0.45% C. +============================================================================== + +¿Cuál es la fase proeutectoide? +------------------------------- +La ferrita. + +¿Cuántos kilogramos de ferrita y de fase proeutectoide se forman? +----------------------------------------------------------------- + +.. raw:: latex + + \[ + W_{ferrita} = \frac {6.67 - 0.45} {6.67 - 0.025} = 0.93 + \Longrightarrow ferrita = 6 kg \cdot 0.93 = 5.6 kg + \] + + \[ + W_{ferrita_{proeutectoide}} = \frac {0.89 - 0.45} {0.89 - 0.025} = 0.51 + \Longrightarrow ferrita proeutectoide = 6 kg \cdot 0.51 = 3.05 kg + \] + + +Bibliografía +============ + +* Diapositivas provistas por la cátedra. +* William D. Callister, Jr. 2000. 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