Issue 62

M. Tedjini et alii, Frattura ed Integrità Strutturale, 62 (2022) 336-348; DOI: 10.3221/IGF-ESIS.62.24

Algorithm 1. Levenberg–Marquardt method [24] begin  : 0 k ;   : 2 ;   0 : x x  : (x) (x) T A J J ;  : (x) (x) T g J f     1 test: g E ;  

    : max ii a ; (E 1 , E 2 and τ are chosen by the user)

while ( not test) and (  max k k )   : 1 k k ; Solve    

  lm h A I g





  lm 2 lm 2 h h E E then

if

test :=true

else

  new lm x : x h     : (x) F F

1 2

  

  







T





g

new (x )

h

h

lm

lm

if   0 then  new x: x

 : (x) (x) T A J J ;      1 test: g E

T : (x) (x) g J f





   3 max 1 3, 1 2 1  

  :

 

;   : 2

else

     : ;     : 2

end

R ESULTS AND DISCUSSION

Tensile test he evolution of the stress with respect to the deformation is presented in Fig. 3. First the material exhibits a linear relationship depicted as Hookean behavior. The slope of the tangent to the stress-strain curve throughout the elastic range is measured (2.9 GPa) and a value of 61 MPa is recorded as a tensile strength at yield elongation (3.40 %). The most important in this curve is the elastic limit 37 MPa to use next as a pilot in the creep experience. SSM Test An initial vertical adjustment is performed to the recorded data. All the creep curves are plotted referring to a constant offset (  0 =0.37 %). However, an increase of strain is observed in each stress jump. In fact, an elastic part which is a real response of the rump function applied in the beginning of each stress is observed between successive stress levels. This elastic strain is measured and eliminated from strain versus time curves of polyamide. Since the elastic modulus is affected after a period of creep, the short term creep curves are adjusted vertically according to the reference [16]. This is achieved graphically by matching every end point of the current strain curve with the start point of the next one, Fig. 4a. So, a series of purely creep curves for each stress level are illustrated in Fig. 4b. However, in order to take into account the stress history and to perform a master curve, a horizontal rescaling of all curves is carried out through the time-axis. The short-term creep results are dependent responses, that reflect a creep behavior under an accumulate stress. These short term curves are extended to the left in order to seeking the rescaling time (t resc ). This is depicted by the required time to achieve the onset of strain (  0 ) for the reference stress. For this purpose, the effect of the curve fitting and the extrapolating functions to approximate this time are analyzed using power, third degree polynomial and exponential models. In order to overcome this problem, the already discussed Levenberg– Marquardt method (Algorithm 1) is used in the present work, taking into account the entire database of measurements ( n  7200). Once the fitting model is aligned to the experimental curve, it is necessary to equalize the expression of the T

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