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Inelastic deformations of stainless steel leaf springs-experiment and nonlinear analysis

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Abstract

A stainless steel leaf spring is designed and constructed followed by its performance evaluation by experiment and non-linear analysis so that an insight into the optimum use of material can be made. Cantilever beams of uniform strength, popularly termed as leaf springs, undergo much larger deflections in comparison to a beam of constant cross-section; that needs inclusions of geometric non-linearity for rigorous analysis. This study deals with such a cantilever beam, but takes into account the material non-linearity as well. Experiments were conducted for such a cantilever beam, with highly non-linear stress-strain curves. In addition to the experiment, a computer code in ‘C’ has been developed using the Runge-Kutta technique for the purpose of simulation. Effective modulus-curvature relations are obtained from the non-linear stress-strain relations for different sections of the beam and used for the analysis. It is seen that non-linear stress-strain curve governs the bending of the beam. Importantly, non-linear analysis shows the stresses are not so high as predicted by the linear theory without end-shortening. Moreover, the tensile and compressive stresses are different in magnitude and both decrease along the span. Experimental load-deflection curves are found to be initially concave upward but, non-linear and convex upward at a high load. Comparison of the numerical results with the available experimental results from another research group and theory shows excellent agreement verifying the soundness of the entire numerical simulation scheme.

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Abbreviations

b0,b:

width of the beam at fixed end and at any point on its span

e :

nominal strain for an axially loaded member

E :

Young’s modulus for the beam material

E″:

effective modulus of elasticity for the beam material

h :

height of the beam

h 1 :

distance from the neutral surface to the lower surface of beam

h 2 :

distance from the neutral surface to the upper surface of beam

I0,I:

moment of inertia of the beam’s cross-section at the fixed end and at any pint on its span.

L :

length of the beam

M,M b :

bending moments

P :

tip load

P 1 :

design load

P 2 :

a tip load higher than P 1

s :

curved length of beam

x :

horizontal distance measured from the fixed end

X H ,X L :

upper and lower limits of x

y :

stressed beam’s transverse deflection

v :

distance from the neutral surface

Z:

section modulus of beam

δ :

tip deflection

δ h :

end-shortening

δ 0 :

difference between original and changed lengths of an axially loaded member

ε :

elongation in the fiber

ε 1 :

elongation in the extreme fiber in the convex side

ε 2 :

elongation in the extreme fiber in the concave side

ε t ,ε c :

true strains in tension and compression, respectively

λ0,λ:

original and changed lengths of an axially loaded member

ρ :

radius of curvature of the neutral surface

Δ:

|ε 1|+|ε 2|

σ :

stress

σ d :

design stress

σ t :

tensile stress in the extreme fiber

σ c :

compressive stress in the extreme fiber

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Authors and Affiliations

  1. Department of Mechanical Engineering, Bangladesh University of Engineering & Technology, Dhaka, 1000, Bangladesh

    Muhammad Ashiqur Rahman & Muhammad Arefin Kowser

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  1. Muhammad Ashiqur Rahman
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  2. Muhammad Arefin Kowser
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Correspondence to Muhammad Ashiqur Rahman.

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Rahman, M.A., Kowser, M.A. Inelastic deformations of stainless steel leaf springs-experiment and nonlinear analysis. Meccanica 45, 503–518 (2010). https://doi.org/10.1007/s11012-009-9270-7

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  • DOI: https://doi.org/10.1007/s11012-009-9270-7

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