#### 3.1. Residual Stress Distribution of Welding Specimens

The strain values at each measurement point of the weldments with the 304 stainless steel welding seam and the Fe-Mn-Si SMAs welding seam were measured by the hole drilling method, and the measured values and the calculated residual stress are shown in

Table 2 and

Table 3. Meanwhile, the distribution curves of the residual principal stress

σ in the direction parallel and perpendicular to the welding seam are shown in

Figure 8.

It can be seen from

Figure 9 that the residual stress distribution laws at the measurement points of the Fe-Mn-Si SMAs welding seam and the 304 stainless steel welding seam are similar in the direction parallel or perpendicular to the welding seam. That is, along the direction of the welding seam, the welding residual stress is tensile stress and gradually decreases from the middle region toward the two sides of the welding seam. In the vertical direction of the welding seam, the residual stress is inversely proportional to the distance between the welding seam and measuring points, and it tends to a zero value [

22].

The in situ formation of Fe-Mn-Si SMAs in the laser welding process was simulated under the same technological conditions, and the distribution of the residual stress in the direction of principal and perpendicular to the welding seam is shown in

Figure 9a,b. It can be seen from

Figure 9 and

Figure 5 that the stress distribution law obtained by simulation and experiment possesses consistent, and the test results and simulation results mutually verify each other’s accuracies. However, some errors still exist, and there are two reasons for this. One reason is that the Gaussian heat source was an ideal heat source, while the surface state of the materials and the distribution of materials elemental components will lead to an uneven energy distribution in an actual laser processing heat source. The other is that the mesh size cannot match distribution size.

To analyze the distributional characteristics of the residual stress and the low residual stress phenomenon of the experimental material, it is necessary to understand the generation mechanism of the residual stress first. The welding seam is a gap before the powder melting and filling it during the laser heating process, so the welding seam only bears the tensile stress of the surrounding base metal in the process of cooling from high temperature. The restrained end of the welding seam changes from a molten-state metal to the solid-state parent metal, so the complicated constraint type is assumed to be elastic constraint, and the contraction strain of the welding seam is represented by

ε_{c} when it cools completely. After the weldment cools to room temperature, the deformation of the welding seam is composed of the following five parts: the thermal strain

ε_{T}, the elastic strain

ε_{e}, the plastic strain

ε_{p}, the transformation strain

ε_{γ}→

_{ε} and the contraction strain

εc. Thus, to analyze the stress and deformation of the welding seam in the cooling process from the high temperature T

_{m} to the room temperature 20°C, the weldment was simplified in a one-dimensional model [

23], as shown in

Figure 10.

In the simplified model of laser weldment, the slender expresses Fe-Mn-Si SMA welding seam, and the two ends are base metals. In addition, the strain variation in the weldment during the laser welding is shown in Equation (1).

where, the thermal strain

ε_{T} and the contraction strain

ε_{c} are caused by temperature reduction and the elastic contraction of base metal, respectively, and both are compressive strain. In addition, the elastic strain

ε_{e}, the plastic strain

ε_{p} and the phase transformation strain

ε_{γ}_{→}_{ε} are caused by the thermal strain, and the sum between the absolute value of

ε_{e},

ε_{p} and

ε_{γ}_{→}_{ε} is equals to the difference between the absolute of

ε_{T} and

ε_{c}. Thus, the strain directions of

ε_{e},

ε_{p} and

ε_{γ}_{→}_{ε} are opposite to that of

ε_{c}, former transition strains are both tensile strain. In this test, the plastic strain that exceeds the elastic strain (yield limit) at room temperature is the residual strain, as shown in Equation (2).

With the law of linear expansion, the thermal strain is shown in Equation (3).

where,

α is the average coefficient of linear expansion of the alloy, and (20 −

T_{m}) is the variable quantity of the temperature in the cooling process of laser welding. According to Hooke’s law, the welding residual stress is shown in Equation (4).

For the same materials (test materials or comparative materials), its phase transformation strain and temperature variation are basically the same in their respective measurement points. Along the direction of the welding seam, the linear expansion coefficient, the elastic limit and phase transition strain of the materials in each measurement point are relatively similar, but the constraint degree in the middle region of the welding seam is more than that in the two sides. Thus, the former contraction strain εc is smaller, and the residual stress is larger in the middle region, and gradually reduces toward the two sides. In the vertical direction to the welding seam, the temperature variation (thermal strain ε_{T}) of the measuring point gradually decreases as it far away from the center of the welding seam, so the welding residual stress gradually decreases.

Although the distribution law of residual stress inside the test materials and the comparative materials are the same, the former residual strain is lower due to its stress-induced martensitic transformation strain

ε_{γ}_{→}_{ε}. The mechanism of the residual stress reduction inside the test materials is shown as follows: under the constrained state of solidified base materials, the residual stress is regarded as a phase transition deformation force to drive crystal orientation a/6 <112>

_{γ} sweeping every other crystallographic plane families {111}

_{γ} in the direction of crystallographic orientation families <112>γ when the residual stress acts on the γ-austenite of the welding seam in the temperature range from the Ms (martensitic transformation starting temperature) to the Md (stress-induced martensitic transformation ending temperature), and the ε-martensite is formed by the single-oriented Shockley imperfect dislocation movement. During the martensitic transformation, the formed ε-martensite can generate three equivalent a/6<112> shear strains

**S**_{1},

**S**_{2}, and

**S**_{3} (with a mutual spacing of 120°) in a {111}

_{γ} habit plane, and the welding residual stress in this test materials will cause the ε-martensite, which produces a macro shearing strain along the

**n** direction (residual stress direction). Supposing the angle of the

**n** direction with the {111}

_{γ} plane and the

**S**_{1} are

θ and

α (

Figure 11), respectively, then Equations of the macro shearing strain caused by equivalent ε variants in one habit plane are shown as Equation (5).

where,

**S**_{0} is the maximum strain caused by a single variant, and its value is equal to 8

^{−1/2} (35.36%).

**S**_{1n},

**S**_{2n} and

**S**_{3n} are the macroscopic strains caused by the shear strains

**S**_{1},

**S**_{2} and

**S**_{3} in the

**n** direction, respectively, and the p

_{1}, p

_{2}, p

_{3} is the generation probabilities of equivalent shearing strains

**S**_{1},

**S**_{2} and

**S**_{3} caused by residual stress in the habit plane. Thus, the total macroscopic strains along the

**n** direction is shown as follows:

**S** =

**S**_{1n} +

**S**_{2n} +

**S**_{3n} =

**S**_{0}·cos

θ·[p

_{1}·cos

α + p

_{2}·cos(120 +

α) + p

_{3}·cos(120 −

α)] [

24]. Because the single ε variant is always formed in the process of stress-induced ε-martensitic phase transformation under most conditions, for instance, p

_{1} = 1, p

_{2} = p

_{3} = 0, then

**S** =

**S**_{0}cos

θcos

α. Meanwhile, the maximum macro shear strain

**S** =

**S**_{0} = 35.36% can be obtained along the direction of

**S**_{1} shearing strain when

θ = 0 and

α = 0. Although the practical condition is different from the ideal condition, and the former macroscopic shearing strain is decreasing in the stress-induced γ→ε martensitic phase transformation, a certain macroscopic strain (0 < S < 8

^{−1/2}) is also present in the experimental materials. In addition, the possible practical conditions are shown as follows: (1) the martensitic phase transition possesses partial cooperation, that is, the phenomenon p

_{1} ≠ p

_{2} ≠ p

_{3}, and

θ ≠ 0,

α ≠ 0; (2) the γ→ε phase transitions are simultaneously performed in several {111}

_{γ} habit planes to form multi-orientation ε-martensite; (3) the orientation of crystal grains in the polycrystalline alloy is different. Through the above analysis, the stress-induced martensitic transformation will cause tensile plastic strain in the direction of the residual stress

ε_{p}. This tensile plastic strain will resist the residual thermal contraction strain, that is, the phase transition deformation can relax the residual strain [

25].

Furthermore, from the aspect of the phase transition free energy in the Fe15Mn5Si12Cr6Ni SMAs, the work in the stress-induced martensite phase transformation (ΔG) is equivalent to the free energy variation in driving the phase transformation. That is, the driving force for the martensitic phase transition can be provided by the external or internal stresses. Therein, the strain in the phase transition process includes two parts: the shearing strain along the habit plane, and the expansion strain perpendicular to the habit plane. Thus, the mechanical driving energy in the aspect of the martensite phase transformation strain can also be expressed in Equation (6) [

26].

where,

σ_{S} is the stress,

ξ is the expansion strain perpendicular to the habit plane,

θ is the angle between the stress and the habit plane, and

α is the angle between the shearing direction and the maximum shear stress, the signs “+” and “−” express tensile stress and compressive stress, respectively.

Thus, the martensitic sheet is first formed along the direction of the maximum ΔG when the residual stress induces the martensitic phase transformation in the multicrystal, and the residual stress is released as a driving force during the lattice generating the shearing strain.

#### 3.2. Bending Fatigue Life of Welding Specimens

Through the bending fatigue test, the 304 stainless steel base metal, the weldment with Fe-Mn-Si SMAs welding seam and the weldment with 304 stainless steel welding seam possess 274, 249 and 136 bending fatigue cycles, respectively, and their macroscopic fracture morphology is shown in

Figure 12. The fatigue cycles of the experimental materials and comparative materials are 49.6% and 90.9% of the base metal, respectively, and it can be seen from

Figure 8 that the fatigue fracture consists of a crack source zone, crack propagation zone and fatigue final rupture zone.

Figure 12 shows that the fatigue cracks originated on the surface of the specimen, and the cracks gradually grew and extruded to form crack propagation zones that are centered on the fatigue crack source under the alternating stress. Then the effective cross section is gradually induced, with the cracks extending, and the specimen immediately fracturing to generate a fatigue final rupture zone when the stress increases beyond the breaking limit. Because three specimens possess similar crack source zones (surface crack source) and crack propagation zones (fatigue striations and few tearing ridges), this won’t be discussed in detail. It can be seen from the macroscopic morphology and the fatigue final rupture zone of each fracture in the

Figure 12 and

Figure 13, and the results are shown below. The macro fracture of the 304 stainless steel base metal is prominent, and the fatigue final rupture zone is significantly higher than the crack source and the crack propagation zone. This is because the base metal has better bending fatigue performance, and the necking occurred in the local area between the metal interfaces and the inclusions in the fatigue final rupture zone. Then numerous microscopic holes are necking, growing, gathering and connecting, and the base metal is finally fracturing and forming uneven dimple-like when the section size of the necking area reduced to a certain extent. This fracture pattern belongs to plastic fracture, and reflects the fact that the base metal possesses better bending fatigue properties [

27]. The macro fracture morphology of the experimental materials is slightly flatter than that of the base metal, and the former fatigue final rupture zone is also composed of dimples. However, the dimples’ depth and number in the experimental materials are less than those of the base metal, so the former bending fatigue characteristics are reduced. Meanwhile, the macro fracture of the weldment with 304 stainless steel welding seam is particularly smooth, and its fatigue final rupture zone consists of a large number of tearing ridges. This fracture belongs to a cleavage fracture (brittle fracture), and its bending fatigue performance is poor.

Compared with the number of bending fracture cycles and fracture morphologies of the test materials and the comparative materials, the former bending fatigue performance is greatly improved. The reasons are as follows: (1) The residual stress inside the Fe-Mn-Si SMAs welding seam is induced martensitic phase transformation in the laser welding process, and the welding residual stress is released to decrease the stress concentration of the welding joint and improve the bending fatigue strength; (2) The Fe-Mn-Si SMAs possess stress self-accommodation characteristics. That is, an additional deformation can be generated by stress-induced γ→ε martensite forward and reverse transformation during the strain cycle, and this deformation in the experimental materials can absorb energy, suppress the plastic slip deformation and reduce the accumulation of dislocations to improve the strain fatigue properties.