New formula cracks rubber fatigue problem that's plagued engineers for decades
Engineers have struggled to predict when rubber components fail because existing fatigue tests vary wildly depending on loading conditions. A new mathematical approach promises consistent predictions regardless of stress patterns, potentially extending the lifespan of everything from car suspension mounts to industrial vibration isolators—and reducing costly field failures.
Originaltitel: Strain-based fatigue capacity and the effective maximum principal (Cauchy) strain of rubber components under R ratios
Many fatigue-damage criteria are widely employed for rubber isolators and have achieved reasonable success under specific loading environments. However, their accuracy is highly influenced by R ratios (the minimum value divided by the maximum value), which pose significant challenges for fatigue assessment in engineering design. In this article, a potential novel methodology, the effective maximum principal strain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mi>e</mml:mi> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , is proposed for fatigue capacity and fatigue evaluations, independent of R ratios. The core concept is to consider both the maximum principal strain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and the maximum principal strain range <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> simultaneously, instead of treating them separately in traditional practice. Both variables should be positive, and fatigue capacity can be related to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> The cylindrical dumbbell specimens, the AE2 samples and an industrial antivibration product were used to validate this methodology. The result demonstrated that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.86</mml:mn> </mml:mrow> </mml:math> was achieved on 30 fatigue cases of the cylindrical dumbbell specimens under both negative and positive R ratios, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.95</mml:mn> </mml:mrow> </mml:math> on 52 cases of AE2 samples under positive R ratios. Additionally, the criterion was applied to the industrial isolator MDS, and crack initiation was calculated at 64.3k cycles, whereas a deep crack was observed at 400k cycles. It has been shown that the fatigue capacity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ε</mml:mi> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> of rubber components is independent of R ratios, which would be beneficial for engineering design in estimating the minimum fatigue life without the need for an extensive fatigue calculation process. The suggested methodology could be easily adopted in industry for engineering design and applications.