Some remarks on the Neuber rule applied to a control volume surrounding sharp and blunt notch tips. (18th November 2013)

• Record Type: Journal Article
• Authors: Zappalorto, M.; Lazzarin, P.
• Is Part Of: Fatigue & fracture of engineering materials & structures. Volume 37:Number 4(2014:Apr.)
• Page Start: 349
• Page End: 358
• Publication Date: 2013-11-18
• Subjects: Materials -- Fatigue -- Periodicals; Fracture mechanics -- Periodicals; 620.1123
• DOI: 10.1111/ffe.12124
• Languages: English
• ISSNs: 8756-758X

Abstract

<abstract abstract-type="main"> <title>ABSTRACT</title> <p>The paper deals with the small scale yielding estimation of nonlinear stresses and strains at the root of sharp and blunt notches through the mechanical model of antiplane shear loadings. The frame stems from the relation existing between the elastic and plastic averaged strain energy densities evaluated over the control volume drawn by the energy contour lines ahead of the notch tip.</p> <p>The analysis proves that there exist different relationships in terms of point‐wise elastic and plastic stresses and strains at the notch tip depending whether the notch is sharp (small notch tip radius) or blunt. For sharp notches, the analysis confirms previous results obtained by the present authors, according to which <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4sxhgm48" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" overflow="scroll" altimg="urn:x-wiley:8756758X:media:ffe12124:ffe12124-math-0001" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>τ</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo stretchy="true">/</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></alternatives>. This equation accounts for the influence of the material law through the hardening exponent <italic>n</italic>. Differently, when the notch can be regarded as blunt, calculations over the control volume give <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4sxhgm5t" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" overflow="scroll" altimg="urn:x-wiley:8756758X:media:ffe12124:ffe12124-math-0002" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi>τ</mml:mi></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi>γ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>t</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math></alternatives>, in agreement with the Neuber rule.</p> </abstract>