FEA modelling approach

The laboratory simulation of magnesium alloy behaviour at bolted joint using FEA tries to reflect real service situation as closely as possible. Previous work [117] used an approach similar to point loading situation to model the stress state with time at bolted joint. This investigation however uses a contact loading approach. For the washer-joint contact model used in this work, the effective stressed area depends mainly on the geometry of the specimen. Important is also the washer that makes the contact to the bolt. The stressed area does not depend directly on the surface of the bolt itself or the nut but on the washers.

The FEA computation of effective stressed area (As) was done by first calculating the stiffness of the joint KJ using equation 48. (F) is the average load and (∆L) is equal to the net displacement on the contact surface of the joint. The

stressed area was then substituted from equation 49 since the elastic modulus

The authors of reference [118] reported an average of 30 % difference between the FEA computed stressed area and that of equation 25. The supposedly underestimation of the stressed area by equation 25 is expected to lower the joint stiffness.

The FEA model applied in this investigation using ADINA [71] assumes that the total deformation (εt) at the AS41 bolted joint is a combination of the elastic strain (εe), plastic strain (εp) and creep strain (εc) as shown in equation 46. From equation 47, it is observed that both the elastic and plastic part is temperature dependent. The plastic strain part of equation 47 can further be expressed as equation 50 [119].

N is the strain hardening exponent. For power law materials, when σys and σucs

are known, the value N can be estimated. The term (a) in equation 51 is approximately equal to 1 at 0.2 % offset yield stress.

It is assumed that the M10 steel bolt and washers used in this work expanded within the elastic regime only, considering the applied temperature. This is approximately 0.1 of the melting temperature of steel bolt. The plastically deformed magnesium alloy due to creep at the exposed temperature causes loss of fastener clamp load on the bolted joint. The degree of loss of clamp load depends among other things, on the operating temperature, stress involved and the compressive creep behaviour of the magnesium alloy.

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In order to take into account the metal temperature change with respect to time, transient thermal analysis was conducted for the simulation. Structural analysis was subsequently performed to evaluate the time dependent bolt load loss as a result of variation in temperature gradient during FE simulation. In the case of AS41 magnesium alloy at 125 °C, the material model to simulate the period of tightening the bolt and putting it into the oil bath was changed from thermal plastic to thermal elastic. This is based on the fact that not all the thermal plastic properties of AS41 alloy were available at the temperatures from 20 °C to 125 °C. Hence a bi-linear relationship was used in the thermal-plastic-creep material model for simulation of the creep regime.

Table 8 compares the FEA prediction in this work with the measured (BLR) after 72 hours for different stress and temperature conditions. The difference between FEA prediction and measured values varies across the load and temperature ranges.

Table 8: FEA prediction and measured (BLR) after 72 hours at test temperature

T (°C) Pre-stress (MPa) FEA (kN) Measured (kN)

40 13.23 12.85 ± 1.00

125 70 15.06 17.16 ± 2.57

40 11.57 9.34 ± 1.13

150 70 14.33 14.06 ± 1.92

40 11.68 9.94 ± 1.67

175 70 12.21 11.82 ± 0.93

The retained load with respect to Pk at 125 °C shows that the model prediction was higher than the experiment by 3.3 % for stress of 40 MPa. In the case of 70 MPa stress, a retained load of 15.06 kN which is equal to bolt load loss of 31.9 % was predicted against 20.2 % measured value. For 150 °C and 175 °C, the model makes higher prediction than the measured value as can be seen from Table 8.

Similar work [118] on HPDC AM50 shows an FEA prediction higher than the measured (BLR) values for an instrumented bolt technique. From equation 47, it is observed that the elastic modulus to a great extent influences the deformation at the bolted joint at elevated temperature. As can be seen from Table 8, the FEA prediction reflects the effect of increasing test temperature on the bolt load retained at Pr after 72 hours. Pr being equal to the bolt load retained at test

temperature as shown in Figure 14. The trend of the FEA prediction is similar to that of measured values as the test temperature increases from 125 °C to 175 °C. See also Figure 89.

Figure 89: Comparative plot of time dependent retained clamp load at bolted joint for 125 °C and 175 °C. Broken lines are model predictions while solid lines are measured values

Possible sources of error may emanate from elevated temperature compression and creep data used in FEA modelling. The influence of porosity on the test samples, amount of second phases clamped by the bolt may also influence the experimental results. In general what can be observed between the FEA prediction and experimental result is the retained bolt load sensitivity to temperature.

From Figure 89, it is observed that different phases of the BLR experiments were reasonably predicted. This includes load increase as a result of thermal expansion difference of the couple during BLR measurements at the inception of the test. The first phase of the slopes which were characterized by prominent bolt load loss was also evident by the model which was consequently followed by asymptotic decrease in retained clamp load. It could be seen that considering the large scatter of the creep and BLR response of permanent mould AS41 magnesium alloy, experiment and model show good agreement.

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