Estimation of the Plastic Zone in Fatigue via Micro-Indentation

Abstract

Accurate knowledge of the plastic zone of fatigue cracks is a very direct and effective way to quantify the damage of components subjected to cyclic loads. In this work, we propose an ultra-fine experimental characterisation of the plastic zone based on Vickers micro-indentations. The methodology is applied to different compact tension (CT) specimens made of aluminium alloy 2024-T351 subjected to increasing stress intensity factors. The experimental work and sensitivity analysis showed that polishing the surface to #3 μm surface finish and applying a 25 g-force load for 15 s produced the best results in terms of resolution and quality of the data. The methodology allowed the size and shape of both the cyclic and the monotonic plastic zones to be visualised through 2D contour maps. Comparison with Westergaard's analytical model indicates that the methodology, in general, overestimates the plastic zone. Comparison with S355 low carbon steel suggests that the methodology works best for alloys exhibiting a high strain hardening ratio.

Keywords: fatigue of materials; micro-indentation; plastic zone in fatigue cracks.

Figure 1

Monotonic stress–strain curve obtained with a tensile test.

Figure 2

An optical micrograph of the 2024-T351 aluminium alloy showing the two principal phases.

Figure 3

Compact tension (CT) geometry of the specimen, manufactured following ASTM standard [29].

Figure 4

CT specimen ready to be cut with a circular saw blade. (a) The grip might induce a force in the crack opening direction. (b) The grip does not induce any load that might affect the fatigue crack plastic zone.

Figure 5

Different indentations as observed in different surface finish. (a) #800 surface finish and indentation obtained with 10 gf, (b) #800 and 25 gf, (c) #1200 and 10 gf, (d) #1200 and 25 gf, (e) #3 μm and 10 gf, (f) #3 μm and 25 gf. All images were taken on a Nikon Epiphot 280 optical microscope with a 100× lens.

Figure 6

Mean hardness measurements obtained with Vickers micro-hardness testing along the crack growing direction for different surface finish and (A) 25 gf and (B) 10 gf. The standard deviation is shown as error bars.

Figure 7

Mean hardness measurements obtained with Vickers micro-hardness testing along the crack opening direction for different surface finish and (A) 25 gf and (B) 10 gf. The standard deviation is shown as error bars.

Figure 8

2D contour maps of micro-hardness around the crack tip for the three specimens: (a) P1, ΔK = 9.91 MPa√m, (b) P2, ΔK = 20.61 MPa√m and (c) P3, ΔK = 30.23 MPa√m. The crack tip is located at coordinates (0, 0) in all maps. The Westergaard theoretical prediction of the monotonic plastic zone is shown as a pink solid line. The theoretical cyclic plastic zone is shown as a pink dashed line.

Figure 9

Micro-hardness profile taken along the crack growing direction for simple P1 (ΔK = 9.91 MPa√m).

Figure 10

Micro-hardness profile taken along the crack growing direction for simple P2 (ΔK = 20.61 MPa√m).

Figure 11

Micro-hardness profile taken along the crack growing direction for simple P3 (ΔK = 30.23 MPa√m).

Figure 12

2D contour map of micro-hardness around the crack tip in a S355 steel. The crack tip coordinates are located at (0, 0).