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12 Fatigue Life Estimation of Polymers R.P.M. Janssen, L.E. Govaert, H.E.H. Meijer Eindhoven University of Technology, Department of Mechanical Engineering

2 Quantitative life time prediction possible, taking thermal history into account. 2 Failure governed by strain softening triggered by accumulation of plastic strain.

Using the plastic strain evolution in the model, this can be solved analytically for a sawtooth signal. 3

10

cycle time

applied stress [Mpa]

true stress [MPa]

quenched

40

0 0

0.25

0.5

0.75

60

50

40

2

4

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10

az =

Impact of the Dynamic Component From cyclic fatigue experiments and simulations having a sawtooth-shape, it appears that (see figure 2): 2 Again quantitative life time prediction is possible. 2 The dynamic component shifts the life time to lower values on the log(t)-axis with increasing amplitude. 65

creep (s =0)

d

55

2

3

10

4

10

5

10

55 σ

ampl

= 0 MPa

50 2 10

3

10

time to failure [s]

4

10

Figure 2 Left: Life time prediction of cyclic fatigue on PC. Right: Numerical simulations indicate a shift in life time due to the dynamic component

Based on the results from the simulation, an impact factor aimpact is defined. This relates the dynamic life time to the life time of the static mean stress, as follows: aimpact =

tf ail,static tf ail,dynamic

It is proposed that such a impact factor can also be derived from the plastic strain γ pl developed during a cycle, as depicted in figure 3a. Since numerical simulations of cyclic fatigue are time-consuming, such an impact factor could save simulation time. aimpact =

8

10

Fatigue simulations, which are performed to validate the analytical result show that the impact factor derived from these simulations closely matches the analytical result. Next to a sawtooth-wave, also simulations of a sine-wave and a square-wave match the derived impact factor, see figure 4a.

σampl = 6 MPa

Time to failure [s]

4 σampl [MPa]6

Remarkably, for this wave-shape only the stress amplitude σampl affects the acceleration factor az . From this analytical approach, it appears that frequency and mean stress do not play a role at all.

σampl = 4 MPa

10

2

60

circles/squares = experimental line = numerical prediction

50 1 10

0

sinh(σampl /σ0 ) (σampl /σ0 )

applied stress [MPa]

mean stress [MPa]

Mean stress [MPa]

constant shift

cyclic (s =4)

= 6 MPa

This approach yields the following impact factor for a sawtooth wave shape:

8

10

time-to-failure [s]

d

σ

Figure 3 Left: Impact of sawtooth signal on mean stress. Right: Impact factor az for a sawtooth signal.

quenched

true strain [−]

60

10

0

time [s]

Figure 1 Left: Intrinsic deformation of quenched and annealed PC. Right: Life time prediction of static fatigue on PC.

65

fails 20x faster 1

70

30 0 10

1

2

10

10 annealed

annealed

mean stress signal

ampl

80 120

80

analytical solution numerical predictions

cyclic stress signal

impact factor [−]

Life time-estimation is imperative for reliable design of polymer components. Previous research showed for static fatigue:

stress [MPa]

Introduction: Static Fatigue

γpl,dynamic (tcycle ) γpl,static (tcycle )

/department of mechanical engineering

σ

(t)

dyn

σ

mean

cycle time time [s]

Figure 4 Left: Impact factor az for a sawtooth, square and sine signal. Right: Any periodic stress signal has impact factor.

Discussion It is shown that cyclic fatigue life time can be estimated from the static life time. Based on the development of plastic strain during a cycle an impact factor was defined. Using this impact factor, failure due to any periodic dynamic stress signal (figure 4b) can be estimated from the plastic strain developed during a cycle. This means that time-consuming simulations can be avoided.

References: [1] K LOMPEN , E.T.J., P H D-T HESIS , TU/ E , 2005 PO Box 513, 5600 MB Eindhoven, the Netherlands