Conclusiones del Tercer Capítulo

The effect of strain rate on forming limit diagrams has been previously studied. The results of (Percy and Brown 1980)and (Lee, et al. 2008) are shown in Figure 6. The first of these shows the forming limit for a panel steel at two loading speeds – and

_{The highest strain rates were given as of the order of . It can be}

seen that this causes a significant change in the shape of the forming limit diagram. The limit is lower between plane-strain and biaxial tension but increases towards uniaxial tension. In comparison, (Lee, et al. 2008) investigated a magnesium alloy, AZ31, at strain rates of and . This showed a fairly consistent drop in formability across all

Page | 12 stress states. (Kim, et al. 2011) found similar, though less pronounced, behaviour for DP590 at strain rates of approximately and .

Figure 6 – Effect of strain rate on forming limit diagram from a) (Percy and Brown 1980) and b) (Lee, et al. 2008)

As such, it is hypothesised that there are three ways for a material’s fracture locus to be strain rate dependent. These are depicted in Figure 7. Firstly, the locus may actually be strain rate independent. Secondly, there could be a uniform change in the fracture strain. The effect of a uniform drop in fracture strain for an increase in strain rate is shown in blue. Finally, the change in fracture strain may be dependent on both the strain rate and strain state. The red line shows a reduction in fracture strain for shear and uniaxial tension, with no change for plane-strain.

Page | 13

Figure 7 – Quasi-static fracture locus of Tata Steel DP800 overlaid with potential effects of strain rate, uniform change in blue, strain state dependent change in red

(Hopperstad, et al. 2003) states that there is no strain rate dependency for a structural steel bar in the range of uniaxial tension to plane-strain. (Panagopoulos and Panagiotakis 1991) investigated the effect of strain rate on the tensile behaviour of aluminium. It was found that fracture strain increased with strain rate for uniaxial tension.

According to (Huh, Kim and Lim 2008), the fracture strain of dual phase steels increases with strain rate in the range of to . However, this is global measurement of a standard tensile test and further work is required to determine the local fracture strain for different stress states.

(Boyce and Dilmore 2009) tested four high strength steels at strain rates between

_{and . It was found that while one alloy would lose of tensile}

ductility across this range, another would gain . This is in terms of global strain of round bar material under uniaxial tension, so may not be directly comparable to this work. However, it raises the point that fracture is potentially sensitive to strain rate and may increase or decrease. 0.0 0.2 0.4 0.6 0.8 1.0 -1.0 -0.5 0.0 Fr ac tu re str ai n alpha

Page | 14

1.2 – Objectives

The first objective of this work is to determine a quasi-static fracture locus, following a similar methodology to those discussed in Section 1.1.2. Some existing processes use a large number of tests to obtain a highly accurate fracture locus. This thesis will use a small set of stress states to calibrate the locus. Assuming the shape can be modelled as a pair of parabolic curves, as suggested by (Bao and Wierzbicki 2004), introduces some uncertainty for a new material. However, it is important to reduce the number of tests required as the main objective of this thesis is to present suitable specimen geometries for determining a fracture locus at multiple strain rates.

The quasi-static fracture locus will be based on three target stress states. These are shear, uniaxial tension and plane-strain, which are the minima and maximum of the fracture locus. These specimens will be designed using finite element analysis and validated experimentally for strain rate and stress state. Following on from this, the specimens will be tested at different strain rates and the effect on fracture strain measured.

The next objective will be to study the thermal behaviour of the geometries at different strain rates to determine if the temperature rise associated with high strain rate deformation has an effect on the fracture strain. It is also important to compare the temperature in the three geometries to validate the specimen design and test methodology. Fractography will be performed to qualitatively assess if a change in strain rate causes a change in fracture mechanism.

The final objective of this thesis is to present a method for producing a strain rate dependent fracture locus. This fracture locus will be a simple mathematical surface fitted to test data rather than a model based on microscopic scale phenomena. The ultimate purpose of this thesis is to develop and validate the methodology for strain rate dependent fracture testing, using the DP800 testing as a baseline.

Page | 15

1.3 – Scope of investigation

1.3.1 – Strain rates

(ten Horn, Carless and van Stijn 2005) and (Huh, Kim and Lim 2008) state that the bulk of deformation in an automotive crash takes place at strain rates of to while (Markiewicz, Ducrocq and Drazetic 1998) gives the range as quasi-static to . As such, the strain rates considered by this work are in the range of to . This includes the quasi-static state that is currently widely investigated, such as (Wierzbicki, et al. 2005), and the high strain rates seen in automotive crash applications. Lower strain rates would be applicable to creep and some specialised forming operations and as such are not considered here.

1.3.2 – Stress states

As described in Section 1.1.1, three data points can be used to calibrate the fracture locus in the tensile region between shear, uniaxial tension and plane-strain. The development of fracture specimens for these conditions is considered in chapters 3 through 5. The rationale for limiting the investigation to this range is discussed below, with compression at a lower value of alpha and biaxial tension at a higher value.

Compression fracture testing, such as carried out by (Bao and Wierzbicki 2004), uses uniaxial compression of short, cylindrical specimens, called the “upsetting test”. An equivalent test in sheet material is more complicated than in bar due to buckling. This can be suppressed, as described by (Boger, et al. 2005), with supporting material. However, this introduces complications arising from correcting the data for friction and resultant forces on the support walls. Furthermore, this experiment is designed to investigate compressive plastic flow and the Bauschinger effect – not fracture. As such, there is no practical way to measure local strains or fracture. In addition, a real-life part such as an automotive crush

Page | 16 can is unlikely to fail in compression. Due to buckling and folding, the strain is largely tensile.

(Bao and Wierzbicki 2005) described a cut-off value for fracture in compression. Fracture is possible between pure shear and uniaxial compression, but not in other compressive strain states. Due to the difficulty in testing in compression and the limited range where fracture is expected to occur, this thesis does not investigate compressive fracture.

Biaxial tension is typically tested through a bulge test. The standard experimental setup is quasi-static, though (Ramezani and Ripin 2010) describes a high strain rate bulge test using a split Hopkinson pressure bar. The setup could be replicated on WMG’s high strain rate testing equipment, described in Section 2.2.2, though it would be difficult to measure the local strain with the apparatus in Section 2.3.5. (Ramezani and Ripin 2010) used thickness reduction of the sheet to measure strain in the sheet. This technique is discussed in 2.3.7 – Tensile strain from thickness reduction but is not suitable for experiments with an uncertain strain state and does not allow the evolution of strain to be mapped.

(Bhatnagar, et al. 2007) developed a test fixture to achieve biaxial loading of sheet in tension. Its design allows for many strain measurement systems to be utilised, such as extensometers or digital image correlation. This system was not used due to the complexities of adding the fixture to a high speed testing machine.