**3.2.1 Aluminium honeycomb**

Cyclic deformation data reveals that honeycomb sandwich panel samples do produce consistent results with acceptable repeatability of results even though the honeycomb core is not a conventional structure due to its complex geometry, but because of its homogeneity, it does compare well to the consistent results we would expect from a less complex conventional aluminium solid sample. The results, also, revealed that samples taken from a longitudinal direction constantly have a longer life expectancy, of approximately 40%, then those samples taken from a transverse direction regardless of environmental exposure.

Deformation Characteristics of Aluminium Composites for Structural Applications 377

By rearranging equation (15) and (16) and separating variables and integrating for m ≠ 2

( 2) ( ) *<sup>f</sup> <sup>m</sup> m m*

<sup>1</sup> *<sup>c</sup> <sup>f</sup> K*

The fracture toughness of aluminium honeycomb sandwich panels is 0.91 MPa *m* and 0.85 MPa *m* for Alulight foam. The calculated crack propagation life versus experimental crack propagation life is shown in Figure 24. In Fig. 24 data can be seen for aluminium honeycomb sandwich panels. The graph clearly shows an excellent correlation between calculated and

> *All Aluminium Honeycomb Sandwich Panel Data*

0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05 *Numbers of Cycles to Failure*

Fig. 24. Calculated Crack Propagation Life versus experimental Crack Propagation Life for

π *YP* ⎛ ⎞ <sup>=</sup> ⎜ ⎟ ⎝ ⎠

*a*

π

*m CY P*

*N*

2 11

= ⎜ ⎟ − − Δ ⎝ ⎠

Before equation (17) could be solved to calculate residual life from a crack size (a*i*) one must know the final or critical crack size (a*f*). For the critical crack condition when *a =* (*af*) equation

*ai a* − −

2

max

( 2)/2 ( 2/2

⎛ ⎞

*f*

Calculated Data Honeycomb Experimental Data Honeycomb

(17)

(18)

gives,

(15) can be rewritten as;

experimental results.

Where*;* K*c*= Fracture Toughness

0.0

Aluminium Honeycomb Sandwich Panel

0.1

0.2

0.3

0.4

*Stress Amplitude (MPa*

0.5

0.6

0.7

Plotting of fatigue data versus stress intensity for aluminium honeycomb sandwich panels shows that samples tested in a corrosive environment are inferior in performance when compared to samples tested in air. Evidence from crack propagation testing establishes that crack propagation takes place, firstly, within the side plate, leading to some fracture but mainly tearing of the honeycomb structure, only a small amount of crack propagation is evident in the honeycomb structure. The weakest part of the sandwich panel structure appears to be the interface between the aluminium side plate and honeycomb core, with the adhesive used being epoxy resin. Crack propagation testing shows that crack growth is not equal on both sides of the sandwich panel structure; this effect must be due to the complex geometry of the hexagonal core and is a potential difficulty when considering the commercial applications of the aluminium honeycomb sandwich panels.

This research produces a valid method of calculating the Paris exponent, m, with the aluminium honeycomb sandwich panel having a Paris exponent, m, of 1.9. This value is similar when compared to typical values for aluminium alloys of between 2.6 to 3.9.

#### **3.2.2 Metallic foam**

Examination of the metallic foam sandwich panel revealed that a consistent form of failure could not be established, with size and position of voids within the metallic foam core having a detrimental effect on failure. Cyclic deformation data revealed that samples tested in air produced inconsistent results showing that the voids within the metallic foam play an important part in crack propagation. However, when samples are tested in an environment, samples taken from the longitudinal direction are superior. This leads to the conclusion that in an environment precipitates within the outer skin have a significant effect on crack propagation. The crack deformation data suggests that due to the complexity of the metallic foam structure and the scatter of results the life of samples exposed to a corrosive environment cannot be correlated with data produced in air. Analysis shows that this is simply untrue and if the two sets of data are plotted a lower and upper trend can be produced, independent of environment and rolling direction, and it is possible to establish a trend of crack growth data within the two bands. This research produced a valid method of calculating the Paris exponent, m. The metallic foam sandwich panel had a Paris exponent, m, of 7.41.

### **3.3 A proposed method of analysis to predict the fatigue life of sandwich panels**

The method of analysis is formed by acquiring the experimental data for aluminium honeycomb and metallic foam sandwich panels. This experimental data is then compared to data produced by calculating the number of cycles to failure. The aim is to calculate the fatigue lives observed experimentally for both aluminium honeycomb and metallic foam sandwich panels. The calculated data will then be used to produce an equation that will predict experimental fatigue life for the complex metallic foam sandwich panels. Conventionally, crack growth rate can be related to the stress intensity factor range using equations (15) and (16).

$$
\Delta K = \mathbf{Y} \left( \Delta P \right) \sqrt{\pi a} \tag{15}
$$

$$\frac{da}{dN} \equiv \mathcal{C} (\Delta K)^m \tag{16}$$

By rearranging equation (15) and (16) and separating variables and integrating for m ≠ 2 gives,

$$N\_f = \frac{2}{(m-2)C(Y\Lambda P\sqrt{\pi})^m} \left(\frac{1}{a i^{(m-2)/2}} - \frac{1}{a\_f^{(m-2)/2}}\right) \tag{17}$$

Before equation (17) could be solved to calculate residual life from a crack size (a*i*) one must know the final or critical crack size (a*f*). For the critical crack condition when *a =* (*af*) equation (15) can be rewritten as;

$$a\_f = \frac{1}{\pi} \left(\frac{K\_c}{Y P\_{\text{max}}}\right)^2 \tag{18}$$

Where*;* K*c*= Fracture Toughness

376 Recent Trends in Processing and Degradation of Aluminium Alloys

Plotting of fatigue data versus stress intensity for aluminium honeycomb sandwich panels shows that samples tested in a corrosive environment are inferior in performance when compared to samples tested in air. Evidence from crack propagation testing establishes that crack propagation takes place, firstly, within the side plate, leading to some fracture but mainly tearing of the honeycomb structure, only a small amount of crack propagation is evident in the honeycomb structure. The weakest part of the sandwich panel structure appears to be the interface between the aluminium side plate and honeycomb core, with the adhesive used being epoxy resin. Crack propagation testing shows that crack growth is not equal on both sides of the sandwich panel structure; this effect must be due to the complex geometry of the hexagonal core and is a potential difficulty when considering the

This research produces a valid method of calculating the Paris exponent, m, with the aluminium honeycomb sandwich panel having a Paris exponent, m, of 1.9. This value is

Examination of the metallic foam sandwich panel revealed that a consistent form of failure could not be established, with size and position of voids within the metallic foam core having a detrimental effect on failure. Cyclic deformation data revealed that samples tested in air produced inconsistent results showing that the voids within the metallic foam play an important part in crack propagation. However, when samples are tested in an environment, samples taken from the longitudinal direction are superior. This leads to the conclusion that in an environment precipitates within the outer skin have a significant effect on crack propagation. The crack deformation data suggests that due to the complexity of the metallic foam structure and the scatter of results the life of samples exposed to a corrosive environment cannot be correlated with data produced in air. Analysis shows that this is simply untrue and if the two sets of data are plotted a lower and upper trend can be produced, independent of environment and rolling direction, and it is possible to establish a trend of crack growth data within the two bands. This research produced a valid method of calculating the Paris exponent, m. The metallic foam sandwich panel had a Paris exponent,

similar when compared to typical values for aluminium alloys of between 2.6 to 3.9.

**3.3 A proposed method of analysis to predict the fatigue life of sandwich panels**  The method of analysis is formed by acquiring the experimental data for aluminium honeycomb and metallic foam sandwich panels. This experimental data is then compared to data produced by calculating the number of cycles to failure. The aim is to calculate the fatigue lives observed experimentally for both aluminium honeycomb and metallic foam sandwich panels. The calculated data will then be used to produce an equation that will predict experimental fatigue life for the complex metallic foam sandwich panels. Conventionally, crack growth rate can be related to the stress intensity factor range using

Δ =Υ Δ *K Pa* ( )

( ) *da <sup>m</sup> C K*

*dN*

π

(15)

≡ Δ (16)

commercial applications of the aluminium honeycomb sandwich panels.

**3.2.2 Metallic foam** 

m, of 7.41.

equations (15) and (16).

The fracture toughness of aluminium honeycomb sandwich panels is 0.91 MPa *m* and 0.85 MPa *m* for Alulight foam. The calculated crack propagation life versus experimental crack propagation life is shown in Figure 24. In Fig. 24 data can be seen for aluminium honeycomb sandwich panels. The graph clearly shows an excellent correlation between calculated and experimental results.

Fig. 24. Calculated Crack Propagation Life versus experimental Crack Propagation Life for Aluminium Honeycomb Sandwich Panel

Deformation Characteristics of Aluminium Composites for Structural Applications 379

*All Sandwich Panel Data* 

Experimental Data Metallic Foam Calculated Data Metallic Foam Experimental Data Honeycomb Calculated Data Honeycomb Calculated Model

Data

1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 *Number of Cycles to failure*

Fig. 26. Calculated Fatigue Life versus Experimental Fatigue Life for Metallic Foam and

The results of both aluminium honeycomb and metallic foam data for both calculated and experimental cycles to failure is shown in Figure 26. An equation was calculated for each set of data, equations 19 for metallic foam and 20 for aluminium honeycomb respectively. The equations 19 and 20 can then be used to develope an equation 21 to predict the fatigue life of a close cell metallic foam sandwich panel. Using equation 21, calculated life for aluminium honeycomb and metallic foam sandwich panels are compared with original experimental data. What is clear from the Fig. 28 is that all of the experimental data for the two types of specimens correlate with the predicted values. The data correlation proves that a successful model is produced to calculate fatigue life for metallic foam sandwich panels. This model is of extreme importance because it shows that from a structural point of view, metallic foam sandwich panels can successfully replace aluminium honeycomb sandwich

0.0

panels.

Aluminium Honeycomb Sandwich Panels

0.1

0.2

0.3

0.4

0.5

*Stress Amplitude (MPa)*

0.6

0.7

0.8

0.9

1.0

However, the calculated crack propagation life versus experimental crack propagation life for metallic foam sandwich panel is shown in Fig. 25 where it can be clearly seen that calculated data does not correlate with experimental data. The graph illustrates that calculated data always produces a higher number of cycles to failure for metallic foam sandwich panels. The main reason for this is that calculation of stress within the metallic foam structure is complex due to the inhomogenity of the voids within the foam. Equations produced using data from Figs. 24 and 25 were then used to calculate experimental data equation for foam:

Foam Calculated:

$$
\sigma = -0.072 \ln N\_f + 1.5518 \tag{19}
$$

Honeycomb calculated:

$$
\sigma = -0.0912 \ln N\_f + 1.3589 \tag{20}
$$

Therefore*,* to plot experimental foam data:

$$
\sigma = \frac{(-0.1632 \ln N\_f - 2.9107)}{2} \tag{21}
$$

*All Aluminium Foam Sandwich Panel Data* 

> Experimental Data Metallic Foam Calculated Data Metallic Foam

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 *Number of Cycles to Failure*

Fig. 25. Calculated Crack Propagation Life versus experimental Crack Propagation Life for

However, the calculated crack propagation life versus experimental crack propagation life for metallic foam sandwich panel is shown in Fig. 25 where it can be clearly seen that calculated data does not correlate with experimental data. The graph illustrates that calculated data always produces a higher number of cycles to failure for metallic foam sandwich panels. The main reason for this is that calculation of stress within the metallic foam structure is complex due to the inhomogenity of the voids within the foam. Equations produced using data from Figs. 24 and 25 were then used to calculate experimental data

0.072ln 1.5518

( 0.1632ln 2.9107) 2 *N f*

= − + *N <sup>f</sup>* (19)

= − + *N <sup>f</sup>* (20)

− − <sup>=</sup> (21)

σ

 0.0912ln 1.3589 σ

σ

Therefore*,* to plot experimental foam data:

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Metallic Foam Sandwich Panels

equation for foam: Foam Calculated:

Honeycomb calculated:

*Stress Amplitude (MPa)*

Fig. 26. Calculated Fatigue Life versus Experimental Fatigue Life for Metallic Foam and Aluminium Honeycomb Sandwich Panels

The results of both aluminium honeycomb and metallic foam data for both calculated and experimental cycles to failure is shown in Figure 26. An equation was calculated for each set of data, equations 19 for metallic foam and 20 for aluminium honeycomb respectively. The equations 19 and 20 can then be used to develope an equation 21 to predict the fatigue life of a close cell metallic foam sandwich panel. Using equation 21, calculated life for aluminium honeycomb and metallic foam sandwich panels are compared with original experimental data. What is clear from the Fig. 28 is that all of the experimental data for the two types of specimens correlate with the predicted values. The data correlation proves that a successful model is produced to calculate fatigue life for metallic foam sandwich panels. This model is of extreme importance because it shows that from a structural point of view, metallic foam sandwich panels can successfully replace aluminium honeycomb sandwich panels.

Deformation Characteristics of Aluminium Composites for Structural Applications 381

related to regular energy release by the material during fracture, indicative of brittle fracture behaviour. On the other hand, the large plastic deformation of the aluminium alloy can be associated with the absence of stress-peaks in conjunction with the monotonic temperature

A model has been applied to predict the interfacial fracture strength of aluminium in the presence of silicon segregation. This model considers the interfacial energy caused by segregation of impurities at the interface and uses Griffith crack-type arguments to forecast the energy change in terms of the coincidence site stress describing the interface and the formation energies of impurities at the interface. Based on Griffith's approach, the fracture toughness of the interface was expressed in terms of interfacial critical strain energy release rate and elastic modulus. The interface fracture toughness was determined as a function of the macroscopic fracture toughness and mechanical properties of the composite using two different approaches, a toughening mechanism model based on crack deflection and interface cracking and a stress transfer model. The model shows success in making prediction possible of trends in relation to segregation and interfacial fracture strength behaviour in SiC particle-reinforced aluminium matrix composites. The model developed here can be used to predict possible trends in relation to segregation and the interfacial fracture strength behaviour in metal matrix composites. The results obtained conclude that the role of precipitation and segregation on the mechanical properties of Al/SiCp

The tension-tension fatigue properties of Al/SiC composites as a function of heat treatment have been discussed as well as the associated damage development mechanisms. The composites exhibited endurance limits ranging from 70% to 85% of their UTS. The T6 composites performed significantly better in absolute values but their fatigue limit fell to the 70% of their ultimate tensile strength. This behaviour is linked to the microstructure and the good matrix-particulate interfacial properties. In the case of the HT1 condition, the weak interfacial strength led to particle/matrix debonding. In the T1 condition the fatigue behaviour is similar to the HT1 condition although the quasi static tensile tests revealed a

The crack growth behaviour of particulate-reinforced metal matrix composites was also investigated. Aluminium A359 reinforced with 31% of SiC particles subjected to two different thermal treatments, as well as wrought aluminium 2xxx series specimens, have been examined using thermographic mapping. Heat treated composites, and especially those samples subjected to T6 aged condition, exhibited different behaviour of crack propagation rate and stress intensity factor range than the as-received composite specimens. Furthermore, the composite specimens exhibited different fatigue crack growth rate characteristics than the base aluminium alloy samples. It becomes evident that the path of fatigue crack growth depends on the heat treatment conditions, where crack propagation relies on strengthening mechanisms, such as precipitation hardening. The microstructure of the interphase region was also found to play a significant role in the crack growth behaviour of particulate-reinforced composites. In this sense, T6 heat treated Al/SiCp composite samples exhibits better interphase bonding behaviour than the other composite systems. The fatigue crack growth curves reveal an approximately linear, or Paris law region, fitting the function da/dN = C ΔK. Crack growth rate vs. stress intensity range curves have been obtained using lock-in thermography. These results are in agreement with crack growth rate measurements using the conventional compliance method and calculations based on the

rise for a large part of the temperature / time curve prior to the specimen failure.

composites is crucial, affecting overall mechanical behaviour.

less ductile nature.
