PSI - Issue 17

C P Okeke et al. / Procedia Structural Integrity 17 (2019) 589–595

592 4

C P Okeke et al / Structural Integrity Procedia 00 (2019) 000 – 000

= 1 1 + 2 2 + 3 3

(3)

where: 1 , 2 and 3 are the actual number of cycles at or below the 1σ, 2σ and 3σ levels respectively. 1 = (0.6831 0 ) , 2 = (0.271 0 ) and 3 = (0.0433 0 ) N 1σ , N 2σ and N 1σ are allowable number of cycles (from fatigue curve) at 1σ, 2σ, 3σ stress levels. These N 1σ , N 2σ , N 1σ are obtained using the S-N relation and the (1σ, 2σ, 3σ) stresses to find the corresponding number of cycles. Narrow Band Formulation: Narrow Band formulation, Miles (1965), Nolte (1976), Chaudhury et al (1985) is a generalised formula where the stress amplitudes are assumed to have a Rayleigh distribution, and every peak is believed to correspond to a cycle. The Fatigue damage is calculated using equation (4): = 0 (√2 ) Г ( 2 + 1) (4) 0 : Statistical frequency, : Exposure Duration, : Equivalent Alternating Stress, Г : Gamma function , : S-N curve properties from the equation, = , where S: Stress Amplitude. Wirsching Formulation: The Wirsching formulation, Wirsching et al (1980), can be expressed as a correction factor to the Narrow Band formulation in order to account for Wideband situation. Rather than using a different, more complicated approach for addressing Wideband scenarios, ANSYS calculates fatigue damage by applying the Wirsching correction factor to the Narrow Band formulation, as shown: = (5) is the wide band correction factor and can be calculated as: = ( ) + [1 − ( )](1 − ) ( ) where: ( ) = 0.926 − 0.033 , ( ) = 1.587 − 2.323 , Ɛ is bandwidth factor: = √1 − 2 is irregularity factor and can be obtained as: = √ 2 0 . 4 0 2 4 are spectral moments, is the fatigue strength exponent obtained from the linear S-N curve. 4. Experiments To obtain the elastic modulus across the stress, a constant crosshead speed of 1mm/min was used to pull the specimen to failure. The dog bone shaped specimens were cut out from an optical plate that was injection moulded at Wipac. The dimensions of the narrow parallel sided portion of the ten specimens tested were 80 x 10 x 2.86 mm. The tensile stress and the elastic modulus were obtained by performing tensile tests under room temperature using Instron 5582 tensile test machine. The stress-strain curve was measured using non-contact video gauge. The random vibration test was performed under room temperature using LDS V721 vibration shaker. The shaker was driven by LDS 5KVA Spak Power Amplifier, and controlled with LDS laser USB controller. The test profile was the same ISO (16750-3) used in simulation. The twelve test specimens used in the experiment were cut-out from PMMA optical blades that were injection moulded at Wipac. The dimensions are 170mm length, 10mm width, and 2.86mm thickness, see fig 2. Each specimen was mounted on a test fixture in a cantilever arrangement as shown in fig 3. The control and response accelerometers used were PCB Piezotronics 353B03 and 352C22 miniature respectively.