Hardening increments in aluminum alloys .
Due to its relative low density and high strength, the 2xxx, 6xxx and 7xxx aluminum alloys series are largely used in transportation industry to produce structural frames and components. These alloys find application in artificial aging condition which allows obtaining high mechanical properties, i.e. yield strength of 7075-T651 aluminum alloy as high as 500 MPa. However, when welding processes are used to perform a junction, a large amount of the heat input is dissipated, by heat conduction, throughout the base material close to the welding bead. This thermal dissipation induces localized isothermal sections where the thermal gradient have an important and detrimental effect on the microstructure and therefore on the mechanical properties of the welded joint (soft zone formation). This microstructural change affects the performance in service of the welded joints, since mechanical properties reduce drastically with respect to base material.
This chapter provides information about mechanical behavior of welded joints of aluminum alloys in terms of properties, determined by tensile, indention and fatigue tests, as well as, the fatigue crack growth conditions in different zones of the welded joints.
1.1. Precipitation and mechanical properties of aluminum alloys
The precipitation hardening process requires that the second component in the aluminum alloy, is sufficiently soluble to allow extensive dissolution at an elevated temperature (solubilization treatment temperature) and that the solubility is considerably reduced at lower temperatures, such is the case of Al-Cu alloys (Figure 1) .
According to Figure 1, to induce precipitation hardening, the alloy is heated at a temperature higher than the solvus temperature to produce a homogeneous solid solution α, allowing dissolution of the second phase θ and eliminates the segregation of the alloy. Once, the solubilization temperature is reached, the alloy is cooling at high rate in order to limit the diffusion process of the atoms toward potential sites of nucleation. Finally, the supersaturated solid solution αss is heated at a temperature below the solvus temperature. At this temperature, the atoms have the ability to diffuse at short distances. Because the αss phase is not stable, the atoms of Cu diffuse at several sites of nucleation and a control precipitation could be formed. Precipitation hardening in metals is performed to produce a particulate dispersion of second phases to generate obstacles for the dislocation movement. The degree of hardening depends of the metallic system, the volume fraction and size of the particles and the interaction of the particles with dislocations. The interactions of the precipitated particles with dislocations are very important in terms of the magnitude of hardening. Some mechanisms have been established, involving particle bypassing by Orowan looping, bypass slip, or particle shearing. Figure 2, shows the forces acting on a mobile dislocation in a stressed metal containing a dispersion of second phase particles.
Considering the equilibrium forces between the line tension T of the dislocation and the resistance force of the second phase particle F, it is obtained:
As F increases, so the bowing of the dislocations increases, i.e. θ increases. The magnitude of F is important in controlling the sequence of events. The dislocation line tension force is maximal when θ=90 º. If the particle is hard, such that F can be greater than 2T, then dislocations will bypass the particle either by Orowan looping or cross-slip and the particle will remain unchanged, i.e. non deformed (Figure 3).
The actual strength of the particle under this circumstance becomes irrelevant, as the bypassing operation becomes dependent only upon the interparticle spacing. If, however, the strength of the particle is such that the maximum resistance force is attained before sin θ=1, then particles will be sheared and the dislocation will pass through the particle (Figure 4).
Therefore, it follows that, for a given interparticle spacing (given volume fraction and particle size), hard particles will give the maximum precipitation hardening, and this condition defines the maximum degree of hardening attainable. Soft particles give a lesser degree of hardening. Consideration of the relationship between the applied stress and the dislocation bowing, following Orowan , leads to the Orowan equation:
where Δτy is the increase in yield stress due to the particles, G the shear modulus of the matrix, b the Burgers vector of the dislocation, and L the particle spacing. The L in the Orowan equation is usually considered to be the distance between particles arranged on a square grid in the slip plane.
Ashby  further developed his equation to take into account the interparticle spacing, and the effects of statistically distributed particles. The Ashby-Orowan relationship is given as:
Application of the Taylor factor for polycrystalline materials, expressing the microstructural parameters in terms of the volume fraction and real diameter and converting shear stress to tensile stress, yields :
where Δσy is the increase in yield strength (MPa), G is the shear modulus (MPa), b is the Burgers vector (mm), f is the volume fraction of particles, and X is the real (spatial) diameter of the particles (mm). Table I presents the hardening effect in terms of yield strength for some aluminum alloys in annealed (O) and artificial age hardened conditions (T6).
|Yield strength (MPa)|
|Alloy||Annealed condition (O)||Artificial age hardened condition (T6)||Difference|
1.2. Welding in age hardened condition
The 2xxx, 6xxx and 7xxx aluminum alloys are known to have a strong tendency to overage during welding, especially in fully aged condition (T6). A schematic representation of the microstructural changes in welding of aluminum alloys is shown in Figure 5 . During welding the adjacent metal to the fusion zone (welding bead) is heated and the heat affected zone (HAZ) contents two principal zones. The zone of lower temperature near to the base metal is exposed to a range of temperatures where the aging phenomena and overaging may occur. The zone of higher temperature is treated by solubilization assuming high cooling rate, the effects are less severe, because the microstructure of the material will tend to age in natural manner. However, and isothermal zone appears at within the HAZ for which the obtained temperature is located between two well defined temperatures, i.e. the artificial aging temperature of the alloy and the solvus temperature. As a result a microstructural transformation takes places due to the thermodynamic instability of the precipitates. For instance, in the case of the 6061-T6 alloy, the over-aging in the HAZ is produced by the transformation of the β’’ (needle shape) precipitates into β’ (rod shape) precipitates according to the following precipitation sequence :
Figure 6, shows the weld thermal cycles for gas metal arc welding (GMAW) process in a 6061-T6 (Al-Si-Mg) alloy at different preheat conditions and their correlation between the C precipitation curve. In this sense, Myhr et al.  studied the microstructural evolution during the cooling weld thermal cycle in Al-Si-Mg alloys (Figure 7). They determined that when the peak temperature Tp approaches 315 °C during a period of time of 10 s, the microstructure consists of a mixture of coarse rod-shape β’ and fine needle-shape β’’ precipitates as shown in Figure 7b and c. The transformation from β’’ to β’ precipitates occurs to an increasing extent with increasing peak temperatures. At Tp of 390 °C the β’ is the dominant microstructural constituent, as indicated in Figure 7d.
In addition to the microstructural transformation, after welding porosity and liquation cracking could also exist, which affect directly the mechanical behavior of the welded joints.
Porosity in welds of aluminum alloys is very complicated to control, because of the high hydrogen diffusion in liquid aluminum (Figure 8), the environmental interaction and the high rate of solidification.
When a fusion welding process in aluminum is performed, the hydrogen diffusion in melted metal could be as high as 1.00 cm3/g, this fact produces the formation of gas bubbles. If we consider the bubble formation in liquid metal as schematically represented in Figure 9, the bubble begins to ascend when the surface tension is overcome by the buoyant force, which tends to push the bubble to the free surface.
The critical radius rc for the separation of the bubble from the solid-liquid interface can be determined by means of the following expression :
where κ is the detaching angle of the bubble, σ* the interfacial energy between liquid and gas (~ 1 Jm-2 for the majority of the gas-metal systems), g the constant gravity force and ρl-ρg the difference between liquid and gas densities. Considering that densities of liquid aluminum and hydrogen at melting point of aluminum are approximately 2380 kgm-3 and 0.0256 kgm-3, respectively, and κ=100°, the rc is roughly 700 μm. It is to say that gas bubbles formed during welding process have to be greater than 700 μm to overcome the surface tension of the solid-liquid interface. Additionally, a low solidification rate is needed to allow the gas bubble coalescence and reach this critical value. However, in a real situation the cooling thermal cycle of the fusion zone in welding, is very fast, as demonstrated in  (Figure 10), and porosity formation is present as shown in Figure 11.
Liquation in welds of aluminum alloys can occur in the partially melted zone (PMZ). The PMZ is the region outside the fusion zone where grain boundary liquation occurs during welding. Figure 12 shows a portion of the PMZ in GMAW of 6061-T6 aluminum made with high silicon content filler metal (ER4043).
The liquation phenomenon occurs along grain boundary, although it can be presented in the grain interior. When liquation is presented, cracking can occur along grain boundary because of the tensile strains generated during welding. The weld metal composition is determined by base metal and filler metal compositions, as well as, the dilution ratio. The dilution ration is related with the amount of filler metal diluted with the base metal to form the weld metal. Metzger  observed liquation cracking in full penetration, gas tungsten arc welding (GTAW) on a 6061 alloy made with Al-Mg filler metal at high dilution ratios, but not in similar welds made with Al-Si filler metals at any dilution ratio. Huang et al.  have conducted studies on liquation cracking in the PMZ of full penetration welds of a 6061 alloy. They found that liquation cracking occurred in GMAW welds when an ER5356 (Al-Mg) filler metal is employed but not with an ER4043 (Al-Si).
2. Mechanical behavior of aluminum alloys welds
The hardness of a material represents the plastic deformation resistance by indentation. The hardness number H, is given by the ratio between the applied load P, and a representative area A, of the residual indent:
For usual indentation, the Vickers hardness number HV, using a pyramidal square based indenter is calculated considering the true contact area. The relation of HV is given by:
where, sometimes, HV is expressed in MPa if P is given in N and d, the indent diagonal, in mm. But usually HV is given as a number and the conditions of load used.
Concerning instrumented indentation tests (IIT), which allow to plot a load-depth curve, the calculation of a hardness number can use the maximum distance (maximum indentation depth hm, reached by the indenter during the indentation test) or the contact depth which is the indentation depth hc, taking into account the deformation of the indent under load and calculated using the method of Olive and Pharr .
Classical indentation has been used to determine the hardness evolution in precipitation hardening aluminum alloys welds [8, 15, 16]. Ambriz et al.  determined Vickers microhardness profiles and mapping representation in welds of 6061-T6 aluminum alloy (Figure 13).
A significant difference for the hardness of weld metal, and HAZ with respect to base material was observed. This indicates that mechanical properties after welding will be different. It should be noted a soft zone formation in both sides of the welded joint, the hardness decrease in the soft zone is around 43% with respect to base material. This characteristic is the result of the thermodynamic instability of the β’’ needle-shaped precipitates (hard and fine precipitates) promoted by the high temperatures reached during the welding process. Indeed the temperatures reached during the welding process are favorable to transform the β’ phase, rod-shaped according to the transformation diagram for the 6061 alloy (Figure 6).
Considering the hardness heterogeneity of the welded joints, instrumented indentation tests (IIT) was performed in base metal, weld metal and HAZ (soft zone). Figure 14, shows the evolution of the applied load as a function of indentation depth for 6061-T6 and 7075-T651 aluminum alloys welds.
Moreover, from the instrumented indentation tests it is possible to calculate the elastic modulus which is deduced by the inverse of the unloading curve (1/S) as a function of the inverse of the contact indentation depth (1/hc) (equation 6).
where is the inverse of the contact stiffness, Cf the frame compliance of the indentation instrument, β geometrical factor introduce in the model of Oliver and Pharr  to take into account the indenter shape and γ the factor introduced by Hay et al.  in the model of Oliver and Pharr for taking into account the approximation in the Hertz’s contact analysis and ER the reduced modulus.
To calculate ER it is needed to determine a corrective factor due to Hay et al. . This coefficient is only dependent on the Poisson’s ratio, then considering a constant value of νm=0.3 for any region of the welded joint (base material, weld metal and HAZ), it is obtained a value of 1.067 for γ. In this condition, the slope is only linked to the reduced modulus by 0.1653/ER. Considering 1140 GPa and 0.07 for the elastic modulus and the Poisson’s ratio for the indenter material, respectively, it is possible to determine the elastic modulus of the different zones of the welded joints (Table II), by means of the following equation:
where Em and νm are the elastic modulus and Poisson’s ratio of the material and Ei and νi the elastic modulus and Poisson’s ratio of the indenter, respectively.
Additionally, the yield strength σy and hardening exponent n can be obtained by indentation tests (Table II) as suggested by Ambriz et al. , by means of the following expression:
where P is the applied indentation load, P0 shift indentation load, E elastic modulus, h true indentation depth into material.
Instrumented indentation test allows to determine the properties given in Table II. Yield strength values determined by instrumented indentation are similar to those obtained by micro-traction test (Figure 16). It means that it is possible to characterize a local zone in a welded material by instrumented indentation where it is not possible by global test (tensile test).
|Material||EIIT (GPa)||σy (MPa)||n||P0 (N)|
On the other hand, the elastic modulus obtained by instrumented indentation does not correspond with those reported in tension or compression tests for aluminum alloys (68-72 GPa) and it is not possible to establish a clear difference between weld metal and HAZ. In fact in a recent study, Chicot et al.  established that the elastic modulus obtained by instrumented indentation corresponds to a bulk modulus. This was explained by the fact that for the case of indentation, the elastic and plastic strain is triaxial, whereas in tensile test, the strain used to determine the elastic modulus is uniaxial.
2.2. Tensile properties
As possible to deduce from indentation test (Figure 13), the tensile mechanical properties of aluminum alloys welds hardened by precipitation, are not homogeneous along the welded joint. Tensile properties in welds obtained by several welding processes of this alloys have been studied. For instance, V. Malin  studied the relation between weld thermal cycles and the microstructural transformation with tensile properties of a 6061-T6 alloy welded by GMAW. In their research, tensile tests samples were taken from the welded joint as shown in Figure 15. It is to say, a global structure effect was considered during tensile test.
The failure zone after tensile test was localized in the HAZ (soft zone) where the hardness of the welded joint is minimal, this result is in agreement with Ambriz et al. .
Considering the hardness profile evolution, the true stress-strain curves in weld metal and HAZ (soft zone) of a 6061-T6 alloy welds were determined by means of micro-traction test . The individual behavior is presented in Figure 16, as well as, its respective comparison with base metal.
The HAZ presents a reduction of the tensile strength with respect to base metal and weld metal of around 41 and 19%, respectively. This aspect was related to the over-aging phenomenon and it is explained in terms of the microstructural transformation (Figure 5), and precipitation sequence. Although, weld metal shows higher tensile strength than HAZ, a lower ductility is observed for weld metal. This characteristic was attribute to the porosity formation during the solidification and the high silicon content of the filler metal (ER4043) which, when mixed with the melted base metal, leads to a microstructure of eutectic silicon, which is a brittle phase that adversely affects the tensile mechanical properties of the welded joint. A summary of tensile mechanical properties for 6061-T6 and 7075-T651 aluminum alloys welds are presented in Table III.
|6061-T6 (weld metal, ER4043)||68||151||226||4.00||464||0.20|
|6061-T6 (HAZ, soft zone)||68||120||183||13.0||300||0.16|
|7075-T651 (weld joint, ER5356)||68||165||260||2.80||677||0.25|
2.3. Fatigue of aluminum alloys welds
Fatigue or fatigue damage is the consecutive modification of the materials properties with respect to the application of a cyclic stress, which can conduct to the fracture. Under uniaxial cyclic loading conditions it is possible to distinguish a stress ratio R determined by a maximal and minimal stress as follow:
As a function of σmax and σmin, we can obtain the constant component of the stress (amplitude stress σa) and the mean value of the stress (mean stress σm) by different loading conditions (Figure 17).
Some practical applications involve cyclic loading at a constant amplitude, but irregular loads as a function of time are commonly encountered. In this case, we will discuss some results in terms of a constant amplitude loading. The simplest fatigue test consists of subjecting a specimen to a cycling loading (different levels of stress amplitude σa), at a constant frequency and measured the number of cycles to failure Nf. The representation of stress level as a function of Nf gives the S-N curve or Wöhler curve. A schematic representation of a Wöhler curve is shown in Figure 18.
In Figure 18, it is possible to identify different domains: (i) Low cycle fatigue. In this case a high stress level is applied on the sample (normally over the yield strength of the material). Because of the high deformation during the test, the number of cycles to failure tends to be lower (102 to 104). (ii) High cycle fatigue. This is related with an elastic behavior on a macro scale of the sample, i.e. the stress level is not higher than the yield strength of the material. The failure is expected for a large number of cycles, for instance, more than 105. In fact the boundary between low and high cycle fatigue is not well defined by a specific number of cycles. The most important difference is that low cyclic fatigue is associated with macro-plastic deformation on each loading cycle. When the stress level in high cycle fatigue is applied, a fatigue limit or endurance limited is presented, which is represented by an asymptote in the Wöhler curve. In some metallic materials it could be obtained when the number of cycles is in the order of 106 to 107. (iii) Fatigue gigacycle. This domain corresponding with a very high number of cycles and it has been observed that fatigue limit tends to decrease when the number of cycles increases.
It is well known that fatigue damage is a surface phenomenon as indicated by Forsyth , who determined the presence of reliefs linked to the formation of localization deformation bands named persistent bands. The surface topography is traduced by the formation of intrusions and extrusions as shown schematically in Figure 19.
For a uniaxial tensile test, these bands resulting in the formation of micro-cracks (state I in Figure 19), which are orientated at 45 degrees with respect the traction axe. Only certain grains are affected by the formation of those bands. The persistent bands orientation and the formation of cracks on the state I, are important in the case of uniaxial and multiaxial loading. Brown and Miller [23, 24] introduced a useful notation in multiaxal loading for facets A and B, which are schematized in Figure 20.
The type B facets provides a shearing vector which enters into the material, and they are more dangerous than type A facets, from which the shearing vector is tangent to the free surface of the sample. The intrusions and extrusions formation associated to the slip persistent bands, as well as, the micro-propagation of cracks in the state I are of interest at a distance of the grain size (small fatigue cracks). Thus, considering that micro-cracks are related with the crystallography aspect, once the crack encounters the first grain boundary it begins to bifurcate according to state II and the propagation at a perpendicular direction of the principal stress is obtained.
Additionally to the fatigue damage mechanism mentioned previously, in the case of welding, the stress concentration factor due to the geometry of the welding bead has a special importance. In this sense, Ambriz et al.  has been quantified the effect of the welding profile generated by modified indirect electric arc (MIEA) technique on the fatigue life of a 6061-T6 aluminum alloy. In order to determine the stress concentration factor Kt in MIEA welds, a characteristic welding profile was measured as specified in Figure 21.
Subsequently, uniaxial fatigue test a cyclic loading with a sinusoidal wave form at a frequency of 35 Hz and load ration R=0.1 was applied in atmospheric air at room temperature. The fatigue limit (77 MPa) was calculated employed the Locati method, and Wöhler curve (Figure 22) was plotted between 77 and 110 MPa.
Figure 22 shows the maximum stress σmax, as function of number of cycles to failure Nf, obtained from the fatigue test of the welded joints. The experimental results were fitted according to the following expression:
where A, and b are experimental values determined by fitting curve.
Regarding the geometry of the welding profile, comparison of the fatigue performance exhibited by MIEA welds with the results reported in the literature  for a single V joint configuration for the same aluminum alloy shows a significant improvement in fatigue life for the MIEA welded samples. The Kt effect on the crack initiation and failure is shown in Figure 23.
The fatigue crack growth rate da/dN, as function of stress intensity factor range ΔK in different zones of the welded joint (base metal, weld metal and HAZ) has been studied previously [26, 27]. The results were conducted on compact type specimens (CT) applying a constant amplitude cycling load with a sinusoidal wave form at a frequency of 20 Hz, a load ratio R of 0.1 and a load range of 2.5 kN in atmospheric air at room temperature. The ΔK was computed by means of the following equation:
where a is the crack length of the sample (initial crack of 8 mm), W the width for the crack propagation, and B the thickness of the sample (5 mm in this case).
Considering the stable crack growth propagation region shown in Figure 24, the experimental results of a were plotted in da/dN versus ΔK graphs according to the following expression:
where C and m are constants obtained from the fitting curve. Table IV summarizes the best fitted values for C and m, and their correlation factor.
Figure 25, shows the fatigue crack growth for base metal (6061-T6) in the rolling and transverse to rolling direction.
This graph shows that the microstructural characteristics (anisotropy) does not have an important influence in terms of fatigue crack growth as could be expected, taking into account that yield strength in rolling direction is higher than transverse direction. However, this is not the case for weld metal and HAZ (Figures 25b and c), in which the crack tends to propagate faster than that in base metal. In the case of weld metal (Figure 25 b), the faster crack growth rate in comparison with base metal is related to the low toughness due to the high silicon (~ 5.5 wt. percent) content provided by the filler metal during welding. Similarly, for the HAZ it is possible to observe that the crack growth is faster than base metal, aspect which is attribute to the microstructural transformation of fine needle shape precipitates β’’ into coarse bar shape precipitates β’ produced by the thermal effect.
Mechanical behavior in welds of precipitation hardened aluminum alloys are still under development and the softening phenomena in the heat affected zone should be better understood. Valuable information could be obtained by the precise understanding of the weld thermal cycles in conjunction with the C transformation curve and its microstructural effect in mechanical properties. In this sense, our research group is conducting experiments to control the weld thermal cycle by means of localized chillers and heaters in the fusion zone and heat affected zone to observe the mechanical properties evolution of the welded joints.