To anticipate central burst defect, and in order to verify the effect of sequentially increasing the strain rate, the simulation consisted of three sequences of eleven drawing processes each. After each sequence, hydrostatic pressure and damage value were analyzed.
3.1 Comparison of principal stresses
Stress can be classified in three major directions. The principal stresses provide useful information in determining the type of stress condition that should be applied to the part. If the absolute value of the first or third major stress is significantly greater than the other two, the solid is either under simple tension or simple compression. When two values are equal, this is a state of equal expansion.
In this case, the analysis of the principal stresses focuses on both σ1 and σ3, the first one allows viewing the areas in tension, whereas σ3 permits to visualize the areas in compression. Therefore, the analysis will focus on the largest positive values for σ1 indicated the strongest pulls, is depicted in the Fig. 3 ((a), (b) and (c)) and the largest negative values for σ3 translated by the strongest compressions is illustrated in the Fig. 3 ((d), (e) and (f)). The distribution of the principal stresses following each pass that precedes the defect creation step is shown in Fig. 4, three types of defects are observed, each of which is different from the other in terms of shape and degree of danger. Regarding the first configuration (range), the phenomenon of line breakers appeared after four passes (Fig. 3a and Fig. 3d). The major cause of this phenomenon can be incorrect tension due to an imbalance of forces between tension and pressure resulting from the accumulation of the previous passes. This result shows that the selection of this range does not meet our needs or the desired objective of studying the drawing process.
The Fig. 3 ((b), (e)) translated the second configuration (range), the deformation increases progressively until the fifth pass. At this point, the strain begins, the wire diameter decreases, and lead to the extra increases of breakage of wire. After the fifth pass, the wire experiences a large increase in stress, which causes the wire to break in the location where the stresses σ1 are at their highest levels. This breaking of the wire causes a tugging action at the wire’s end.
The third configuration (range) is different in terms of shape and severity of the defects (Fig. 3c and Fig. 3f). As a result of the absence or reduction of hydrostatic tension in the wire's center, it has been demonstrated [2, 13, 31] that such hydrostatic tension stress results in central porosity and central void along the cross-section of the billet.
3.2 Hydrostatic pressure
Pressure field in drawing processes can be used to highlight the appearance of core defects. These defects can be generated according to several criteria such as die angle or reduction rate. The hydrostatic pressure p is defined as the third of the stress tensor trace, i.e., as the average of the diagonal terms:
$$p= - \frac{1}{3}tr\left( {\left[ \sigma \right]} \right)= - \frac{{{\sigma _{11}}+{\sigma _{22}}+{\sigma _{33}}}}{3}$$
6
This field allows us to know if the zones are in compression (p > 0) or in tension (p < 0).
In the first case, we notice a zone of the wire core reaches its critical damage value (CL = 0.84) along the axis of the drawn wire, this result predicted a clear potential risk of central rupture for the wire as material flow will be faster at the wire edges than at its center. On the other side and regarding to results showed in the Fig. 4 ((b), (c)), it is clarified that the predicted damage value gradually increases towards the drawing axis and localized in the wire core. However, there is a region where the damage value exceeds the critical value, which means that until the fourth pass, there is no central bursting occurs under this combination of process parameters, and the measurements value of damage for all passes are summarized in Table 4.
Table 4
The values of the damage computed for each step of the three drawing ranges investigated.
Pass
|
ø
rang1
|
total r %
|
r per pass
%
|
damage
rang1
|
ø
rang2
|
total r %
|
r per pass %
|
damage
rang2
|
ø
rang3
|
total r %
|
r per pass %
|
damage
rang3
|
1
|
7.66
|
35
|
35
|
0.28
|
8.25
|
24.67
|
24.67
|
0.17
|
8.91
|
12
|
12
|
0.12
|
2
|
6.28
|
56.37
|
32.87
|
0.47
|
7.16
|
43.25
|
0,35
|
8.24
|
24.72
|
14.45
|
0.24
|
3
|
5.22
|
69.78
|
30.75
|
0.67
|
6.21
|
57.25
|
0.50
|
7.51
|
37.45
|
16.91
|
0.38
|
4
|
4.41
|
78.43
|
28.62
|
0.84
|
5.39
|
67.80
|
0.70
|
6.75
|
49.56
|
19.36
|
0.52
|
In the second part, and according to the three-dimensional analysis of the hydrostatic pressure illustrated by the right column of Fig. 4 ((a), (b), (c)), it showed us that the positive hydrostatic stress value predominates around the central part of the deformed wire, indicating that localized void nucleation occurs along the axis of the drawn wire. It is noticed that the normal hydrostatic stress decreases progressively from the center of the wire toward the edges in a direction perpendicular to that of the drawing. Also, a negative hydrostatic pressure value on the wire walls indicates a tensile load effect, due to the wire material sticking to the die wall.
In addition, the normal pressure distribution in the transverse direction is also undulating. Therefore, the state of stress is considered an important parameter for central bursts, which is estimated by the distribution of hydrostatic pressure around the central area of the deformed part.
Finally, the numerical simulation results made it possible to control how a combination of process parameters will cause a central bursting of the drawn wire, this is what was observed in the first range and to a lesser extent in the second range, while the wire in the third range remained to complete its trajectory with success until the next pass.
3.3 Prediction of central burst defect geometry
Central burst defects (also known as chevron defects) are common in the electrical cable industry. These defects can only be identified through visual inspection. They propagate from an internal crack in the billet due to the presence of hydrostatic tensile stress along the boundary of the deformation zone. Die angle (α), reduction ratio (r), and friction coefficient (µ) are the primary factors significantly influencing the formation of central burst defects. The objective was to determine the limiting values of the Cockroft-Latham integral for three wire drawing ranges.
Remmers experiment [12] is used to simulate the same material grade and variables (α, r, µ) that influence the formation of central burst defects. The current solution is then evaluated for its validity and effectiveness. Remmers discovered chevron cracks and holes between the cracks in the center of a copper wire drawn in 8 sequential dies with a total area reduction of 67.6% (Fig. 5a). The numerical simulation shows that the central burst (chevrons) initiates in the core of the wire (Fig. 5b).
It can be clearly seen that the damage values increase gradually with the increase of the number of drawing passes. Furthermore, the damage evolution in the drawing process shows evident non-linear characteristics. The damage distribution in the axial and circular directions corresponds well with Remmers' experimental study [12] as shown in Fig. 5.
The numerical simulation was carried out until the material failed. Subsequently, an analysis was performed on three distinct ranges of wire drawings, wherein an examination of the final diameters achieved, the strain rate, and the numbers of passes were undertaken. The tabulated data presented in Table 3 reveals the observed outcomes of this investigation. It is important to note that the fracture characteristics differed within the specified ranges: ranges 1 and 2 exhibited cuppy wire fractures, while the third range displayed central burst fractures, commonly referred to as chevron fractures.
The first range starts at a 35% strain rate as shown in Fig. 6A. The predicted damage value gradually increases towards the extrusion axis and the outer periphery, but it is quite below the critical damage value in the first four passes. This means that no central burst occurs under these four passes. During the fourth pass, the damage value increases significantly and reaches a value of 0.84 in the core of the wire, close to the critical value, and this just after four passes. This is due to a substantial reduction rate of ε = 78.43%, spread over four passes alone, resulting in rapid and sudden hardening. In the fifth pass, the accumulation of tensile force will cause material tearing at the mandrel/wire interface.
In the second range (Fig. 6B) where the deformation rate of 24% is equal between all passes, and with a total strain rate of 81.73% distributed over 6 passes, we recorded the damage values CL in the following order for each pass sequence: 0.1685, 0.3454, 0.5, 0.6990, 0.8177, 1(max). Within this range, a "new defect" known as "cuppiness" emerges. This defect does not appear to be specific to a particular metal or alloy but seems to occur at different times in all drawn materials. Some researchers have hypothesized that the source of the problem lies in overloading the wire, and that the presence of inclusions in the wire can create weak zones, and that the deformation rate is significant between passes. And this is the focus of our research study.
In range 3, the damage values from the 1st pass to the 6th pass are sequentially: 0.11, 0.24, 0.37, 0.52, 0.69, 0.85 and the chevron occurrence is located just after the 6th pass with a value of 1, which indicates the full damage. A special kill element function was implemented to show a macro central burst defect (Fig. 6C), which shows micro-crack initiation after the 7th pass in the form of a discontinuous central burst along the thread axis. On the 8th pass, a tear was observed at the contact between the wire and mandrel.
It has been demonstrated that back tension intensity has a significant impact on cumulative damage. As a result, back tension increases the likelihood of a central bursting defect even though it lowers the interfacial stress between the die and the material. The nucleation of voids is induced by the concentration of maximal stresses in the wire's core, while the growth and coalescence of voids are caused by crack propagation.
Figure 7 shows the effect of the number of passes on wire breaks when the reduction ratio varies within the three ranges, the damage value for the three ranges is determined within the wire’s core based on the amassed strain, it reach the value of the damage of 0.8 after four pass for the range 1, but it’s not satisfied the desired value of the wire diameter (4.41 mm) which is quickly reaches the critical damage value in range 1 and less in range 2, while in the third range continues along a linear curve.
The wire drawing process requires the application of a sufficient force, which is translated into the plastic deformation power, also called the plastic power, the quantification of which is an index used to calculate the energy required by the wire to go from the initial state D0 to the next step D1 to the final state Df as a function of time.
The contrast visible on all curves in the Fig. 8a-e shows the magnitude of the effect of the strain rate variation for each drawing range. Therefore, less energy consumption is noticed in the third range, because the value of the strain rate in this range is the lowest compared with the other ranges. The lowest point value in range1 after three passes (Fig. 8c) indicates the drop in plastic power, it represents the beginning of the formation of a central bursting defect, also known as chevron, which indicates that the defect size is significant. The chevron continues to increase until the wire breaks in the fifth pass (see Fig. 8e and Fig. 6A).
For the second configuration, the wire continues to the next pass with the appearance of fluctuations in the plastic energy curve which disappear at the fifth pass without any visible defects as shown in Fig. 8 ((d), (e)).
On the other hand, in the third configuration, there are no internal bursting defects, and this is reflected in the absence of any drop along the plastic energy curves of all passes, as shown in Fig. 8. This is due to the low strain rate, which started at 12% in the first pass and increased to 60% in the fifth pass.
The objective was to find out how the strain rate affected the energy needed for wire drawing. According to the computation, the activation energy of the fourth pass in range 2 decreases gradually with increasing strain, resulting in a softening of the heat-induced flow. The negative peak signifies the appearance of a chevron, with only range 3 managing to perform all these five passes flawlessly.