<content> <p>Tabelas e fórmulas da Seção 6.6</p> </content>

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&[DATE] &[TIME] - &[FILENAME]

EXEMPLO 6-1

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Determinação de diagramas S-N estimados para materiais ferrosos

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Problema

Construa um diagrama S-N estimado para uma barra de aço e defina suas equações. Quantos ciclos de vida podem ser esperados se a tensão alternada é de 100 MPa?

Dados

O S_ut obtido experimentalmente é 600 MPa. A barra quadrada tem 150 mm de lado e tem acabamento superficial de laminado a quente. A temperatura máxima de operação é de 500°C. O carregamento aplicado é flexão pura alternada.

Hipóteses

A vida infinita é requerida e pode ser obtida, pois este aço dúctil apresentará limite de fadiga. Será considerado um fator para confiabilidade de 99,9%.

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S.ut 600 MPa * : σ.max 100 MPa * : σ.min 100 MPa * : 13 mat

Solução:

1) Como nenhuma informação sobre o limite de fadiga ou resistência à fadiga é fornecido, estima-se S_e'com base no limite de ruptura usando a Equação 6.5a.

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(a) S.e' 0.5 S.ut * : MPa 300

3) A peça é maior que o corpo de prova e não tem seção circular, portanto um diâmetro equivalente baseado em 95% da tensão máxima (A₉₅) deve ser determinado e usado para encontrar o fator de tamanho. Para uma seção retangular sob flexão sem rotação, a área A₉₅ é definida na Figura 6.25c e o diâmetro equivalente é obtido por meio da Equação 6.7d:

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b 150 mm * :

h 150 mm * :

A.95 0.05 b * h * : mm 2^1125

(c) d.b A.95 0.0766 / sqrt : mm 121.2

Tabela.secao6 Polegada Métrica 21 mat :

"Polegada"
"Métrica"

Unidade de Medida:

B <content> <p>Tabelas e fórmulas da Seção 6.6</p> </content>

Equações 6a@d - Páginas 329 e 330 Limite_Fadiga.1 Aços 0.5 S.ut * 700 MPa * 1400 MPa * Ferros 0.4 S.ut * 160 MPa * 400 MPa * Alumínios 0.4 S.ut * 130 MPa * 330 MPa * Ligas de Cobre 0.4 S.ut * 100 MPa * 280 MPa * 44 mat :

Equação(6.7a) - Página 330 C.carreg.matrix Flexão 1 Força Normal 0.7 22 mat :

Equação (6.7b) - Página 331 C.tamanho.matrix para d ≤ 0,3in (8mm) 1 para 0,3in < d ≤ 10in 0.896 d.b in / (0.097 -^* para 8mm < d ≤ 250mm 1.189 d.b mm / (0.097 -^* 32 mat :

Tabela 6-3 - Página 333 B 1 el Métrica ≡ CS 1.58 0.085 - 4.51 0.265 - 57.7 0.718 - 272 0.995 - 42 mat : CS 1.34 0.085 - 2.7 0.265 - 14.4 0.718 - 39.9 0.995 - 42 mat : if

Coeficiente_Superficie.matrix Retificado CS 11 el CS 12 el Usinado ou Estirado a Frio CS 21 el CS 22 el Laminado a Quente CS 31 el CS 32 el Forjado CS 41 el CS 42 el 43 mat :

Coeficiente_Superficie.matrix Retificado 1.58 0.08 - Usinado ou Estirado a Frio 4.51 0.26 - Laminado a Quente 57.7 0.72 - Forjado 2721 - 43 mat

Equação 6.7f - Página 335 C.temperatura.matrix T ≤ 450°C (840°F) 1 para 450°C < T ≤ 550°C 1 0.0058 T °C / 450 - (* - para 840°F < T ≤ 1020°F 1 0.0032 T °F / 840 - (* - 32 mat :

Tabela 6-4 - Página 335 C.confiabilidade.matrix 50190 0.897 95 0.868 99 0.814 99.9 0.753 99.99 0.702 99.999 0.659 99.9999 0.620 82 mat :

"Aços"
"Ferros"
"Alumínios"
"Ligas\0020\de\0020\Cobre"

Limite de Fadiga não Corrigido:

Limite_Fadiga.2

Limite_Fadiga.2 Aços 3108^* kg m s 2^* / * 7108^* kg m s 2^* / * 1.4 109^* kg m s 2^* / * 14 mat

S.ut Limite_Fadiga.2 4 el < S.e' 0.5 S.ut * : S.e' Limite_Fadiga.2 3 el : if

S.e' MPa 300

"Flexão"
"Força\0020\Normal"

Fator devido à solicitação:

C.carreg

C.carreg 1

"para\0020\d\0020\\2264\\0020\0\002C\3in\0020\\0028\8mm\0029\"
"para\0020\0\002C\3in\0020\\003C\\0020\d\0020\\2264\\0020\10in"
"para\0020\8mm\0020\\003C\\0020\d\0020\\2264\\0020\250mm"

Fator de Tamanho:

C.tamanho

ATENÇÃO! FALTA INSERIR DIÂMETRO EQUIVALENTE PARA PERFIS
DIFERENTE DE REDONDOS (VER PAG.333)

d.b mm 121.19

d.b in 4.77

C.tamanho 0.747

"Retificado"
"Usinado\0020\ou\0020\Estirado\0020\a\0020\Frio"
"Laminado\0020\a\0020\Quente"
"Forjado"

Tabela 6-3 Coeficientes para a equação do fator de superfície:

Coeficiente_Superficie

A Coeficiente_Superficie 2 el : 57.7

b Coeficiente_Superficie 3 el : 0.718 -

B 1 el Métrica ≡ C.superficie A S.ut MPa / (b^* : C.superficie A S.ut ksi / (b^* : if 0.584

C.superficie 0.584

"T\0020\\2264\\0020\450\00B0\C\0020\\0028\840\00B0\F\0029\"
"para\0020\450\00B0\C\0020\\003C\\0020\T\0020\\2264\\0020\550\00B0\C"
"para\0020\840\00B0\F\0020\\003C\\0020\T\0020\\2264\\0020\1020\00B0\F"

Fator de Temperatura:

C.temp

T 500 °C * :

C.temp 0.71

50
90
95
99
99.9
99.99
99.999
99.9999

Fator de Confiabilidade:

C.conf

C.conf 0.753

Limite de Fadiga não Corrigido: S.e' MPa 300

Limite de Resistência Corrigido: S.e S.e' C.carreg * C.tamanho * C.superficie * C.temp * C.conf * :

S.e MPa 70

8) Para criar o diagrama S-N é necessário estimar a tensão Sm em 103 ciclos de acordo com a Equação 6.9 para flexão.

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(i) S.m 0.9 S.ut * : MPa 540

9) O diagrama S-N estimado é mostrado na Figura 6-34 com os valores de S_m e de S_e acima. As equações das duas linhas são obtidas pelas Equações de 6.10a a 6.10c assumindo que S_e começa aos 10⁶ ciclos.

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(j) b 13 / S.m S.e / log10 * - : a S.m 103^(b^/ : 21 line

a MPa 4169.31

b 0.29589 -

a

S.e S.e MPa / : 69.94

a a MPa / : 4169.31

N 103^109^104^range :

(k) N S N 103^106^lelt a N b^* S.e if :

10 5.9^S 74.870864

106^S 69.939713

10 6.1^S 69.939713

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x S 100 S.e 3 1 sys

10) O número de ciclos de vida para qualquer nível de tensão alternada pode ser determinado com as Equações (k). Para a tensão alternada aplicada de 100MPa tem-se:

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\[REGION[c9095248025f4bd898dff4022df25115]]\ ciclos

N.1 100 a / (1 b /^: 3105^*

A Figura 6-34 mostra a interseção da linha de estresse alternado com a linha de falha em N = 3E5 ciclos.

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