Influence of Impact Velocity on the Residual Stress, Tensile Strength, and Structural Properties of an Explosively Welded Composite Plate

This study aimed to analyze the effect of the impact velocity of a Zr 700 flyer plate explosively welded to a Ti Gr. 1/P265GH bimetallic composite on the residual stress formation, structural properties, and tensile strength. The residual stresses were determined by the orbital hole-drilling strain-gauge method in a surface layer of Zr 700 in as-received and as-welded conditions. The analysis of the tensile test results based on a force parallel to interfaces was used to propose a model for predicting the yield force of composite plates. Compressive residual stresses found in the initial state of the Zr 700 plate were transformed to tensile stresses on the surface layer of the welded Zr 700 plate. A higher impact velocity resulted in higher tensile stresses in the Zr 700 surface layer. To increase the resistance of the composite plate to stress-based corrosion cracking, a lower value of impact velocity is recommended in the welding process.


Introduction
Metallic composites belong to a group of materials in which the multilayer structure of different metallic alloys provides special functional properties [1]. Explosive cladding is one of the manufacturing processes used to produce multilayer metallic composites. It involves the energy of detonation to accelerate a flyer plate that, as a result, collides with a base plate [2,3]. High-velocity impact leads to the formation of a strong bond between colliding plates. Low-density materials, such as aluminum and magnesium alloys, can be explosively welded to steels and applied in the ship building and automotive industries [4,5]. A copper layer [6,7] within a composite multilayer material provides excellent electrical conductivity, and so-called reactive materials such as titanium [8,9], zirconium, and niobium exhibit corrosive resistance in an aggressive environment. This, in turn, predisposes them to wide usage in design applications in process equipment in particular [10]. A composition of tungsten foil and cooper layers is applicable for thermonuclear reactors [11] since it offers high resistance to heat loads and irritation.
Zirconium exhibits outstanding performance as a material for use in highly corrosive environments with a broad range of chemical media and temperatures [10,12,13]. This allows the material to be used in the chemical process industry for heat exchangers cooled with seawater and other pieces of process equipment as well as in nuclear-fuel-reprocessing plants. To reduce the financial cost of tensile tests were conducted with force applied in the parallel direction to the interface. Moreover, a model for predicting the yield force of the composite plate is proposed.

Materials in As-Delivered Condition
A composite structure consisting of three layers made of P265GH pressure vessel steel, Ti Gr. 1, and zirconium Zr 700 was manufactured in the explosive welding process. Tables 1 and 2 summarize the chemical composition and mechanical properties of the materials examined in this study, respectively. The tensile tests were conducted to estimate the presented mechanical properties. Table 1. Chemical composition of materials in as-delivered conditions [35].

Materials
Chemical Composition (wt %) E is the elastic modulus, ν is Poisson's ratio, A is the elongation, R p02 is the yield strength, and R m is the tensile strength.
The microstructure of the materials under as-delivered conditions is illustrated in Figure 1.
Materials 2020, 13, x FOR PEER REVIEW 3 of 14 tensile tests were conducted with force applied in the parallel direction to the interface. Moreover, a model for predicting the yield force of the composite plate is proposed.

Materials in As-Delivered Condition
A composite structure consisting of three layers made of P265GH pressure vessel steel, Ti Gr. 1, and zirconium Zr 700 was manufactured in the explosive welding process. Tables 1 and 2 summarize the chemical composition and mechanical properties of the materials examined in this study, respectively. The tensile tests were conducted to estimate the presented mechanical properties. Table 1. Chemical composition of materials in as-delivered conditions [35].

Materials
Chemical Composition (wt %) is the elastic modulus, is Poisson's ratio, is the elongation, 02 is the yield strength, and is the tensile strength.
The microstructure of the materials under as-delivered conditions is illustrated in Figure 1. The microstructure of Zr 700 plate in the section perpendicular to the rolling direction is presented in Figure 1a. The material was characterized by the structure of the α-phased grains sized between 70 and 170 µ m. The microstructure of the material used in the interlayer, i.e., Ti Gr. 1 alloy, consisted of α-phased equiaxed grains sized between 20 and 40 µ m (Figure 1b). Figure 1c presents the P265GH carbon steel microstructure characterized by an equiaxed structure of mid-sized grains of 4-11 and 10-20 µ m for pearlite and ferrite, respectively. As shown, a band structure composed of fine grains of pearlite was observed; this is a typical phenomenon for materials after the hot-forming process. The microstructure of Zr 700 plate in the section perpendicular to the rolling direction is presented in Figure 1a. The material was characterized by the structure of the α-phased grains sized between 70 and 170 µm. The microstructure of the material used in the interlayer, i.e., Ti Gr. 1 alloy, consisted of α-phased equiaxed grains sized between 20 and 40 µm (Figure 1b). Figure 1c presents the P265GH carbon steel microstructure characterized by an equiaxed structure of mid-sized grains of 4-11 and 10-20 µm for pearlite and ferrite, respectively. As shown, a band structure composed of fine grains of pearlite was observed; this is a typical phenomenon for materials after the hot-forming process.

Explosive Welding Process
The explosive welding process was conducted by High Energy Technology Works "Explomet" (Opole, Poland). Consequently, two multilayer plates were produced with different welding parameters. In both cases, the flyer plate made of Zr 700 with a thickness of 10 mm was cladded to the preliminary welded bimetallic plate composed of a 2-mm Ti Gr. 1 layer and a 14-mm P265GH steel layer. The plates with dimensions of 300 mm × 500 mm were welded in parallel by applying an explosive charge of ammonites, with NH 4 NO 3 (High Energy Technology Works "Explomet", Opole, Poland) as the main component. The detailed composition of the explosive charge was not provided by the supplier of the composite plates. The applied explosive charge resulted in a detonation velocity of v D = 2500 m/s, which was measured using a fiber optic system [36]. The welding processes for the studied plates have different values of stand-off distance δ (which is the initial distance between the flyer plate, Zr 700, and the basic Ti Gr. 1-P265GH bimetal). For the first plate, labeled as B3, the stand-off distance was δ = 10 mm, whereas it was δ = 15 mm for the second plate (B4). The application of different δ values resulted in different impact velocities v P estimated using the Deribas formula [37,38]. The summarized welding parameters are presented in Table 3. Both the welded plates underwent the flattening process and ultrasonic examination [39], revealing no discontinuities except near the ignition and narrow area at the plate edges (approximately 20 mm from the edge). Figure 2 shows the locations of the ignition point and samples used for residual stress measurement and microstructural analysis.

Explosive Welding Process
The explosive welding process was conducted by High Energy Technology Works "Explomet" (Opole, Poland). Consequently, two multilayer plates were produced with different welding parameters. In both cases, the flyer plate made of Zr 700 with a thickness of 10 mm was cladded to the preliminary welded bimetallic plate composed of a 2-mm Ti Gr. 1 layer and a 14-mm P265GH steel layer. The plates with dimensions of 300 mm × 500 mm were welded in parallel by applying an explosive charge of ammonites, with NH4NO3 (High Energy Technology Works "Explomet" , Opole, Poland) as the main component. The detailed composition of the explosive charge was not provided by the supplier of the composite plates. The applied explosive charge resulted in a detonation velocity of = 2500 m/s, which was measured using a fiber optic system [36]. The welding processes for the studied plates have different values of stand-off distance δ (which is the initial distance between the flyer plate, Zr 700, and the basic Ti Gr. 1-P265GH bimetal). For the first plate, labeled as B3, the stand-off distance was δ = 10 mm, whereas it was δ = 15 mm for the second plate (B4). The application of different δ values resulted in different impact velocities estimated using the Deribas formula [37,38]. The summarized welding parameters are presented in Table 3. Both the welded plates underwent the flattening process and ultrasonic examination [39], revealing no discontinuities except near the ignition and narrow area at the plate edges (approximately 20 mm from the edge). Figure 2 shows the locations of the ignition point and samples used for residual stress measurement and microstructural analysis.

Residual Stress Estimation
Residual stress was identified using the incremental hole-drilling strain-gage method recommended in the ASTM E837-13a standard [34], and the experiments were conducted on the surface of the flyer Zr 700 plate. Additionally, for referential analysis, residual stresses in the Zr 700 plate in the as-delivered condition were estimated.
For measuring the relieved strains during incremental hole drilling, a Vishay RS-200 device (Vishay Precision Group, Malvern, PA, USA) with a pneumatic turbine was used in orbital drilling

Residual Stress Estimation
Residual stress was identified using the incremental hole-drilling strain-gage method recommended in the ASTM E837-13a standard [34], and the experiments were conducted on the surface of the flyer Zr 700 plate. Additionally, for referential analysis, residual stresses in the Zr 700 plate in the as-delivered condition were estimated.
For measuring the relieved strains during incremental hole drilling, a Vishay RS-200 device (Vishay Precision Group, Malvern, PA, USA) with a pneumatic turbine was used in orbital drilling mode. This method appears to be beneficial in several ways, one of which is the considerable improvement of drilling conditions [40]. In addition, a Vishay milling cutter (Vishay Precision Group, Malvern, PA, USA) was used for the drilling and producing holes with the final diameter of approximately 1.9 mm. The holes were drilled in incremental steps of 0.05 mm to a total depth of 1 mm. This study employed a three-element type-A [34] strain rosette gauge of FRS-2 (TML Lab. Company, Tokyo, Japan), paired with a multi-channel signal-acquisition device (P3 Strain Indicator and Recorder, Vishay Precision Group, Malvern, PA, USA) (with resolution of strain measurement equal to 10 −6 ). Four measurement points were located in the middle part of plate B3 and two on plate B4. The distance between the points varied from 30 to 70 mm. Additional residual stress estimation for the Zr 700 plate under the as-delivered condition was based on two measurement points.

Structural Properties
The process of explosive welding is characterized by the formation of an interface between the periodic deformation and the interfacial wave [3] (Figure 3a). mode. This method appears to be beneficial in several ways, one of which is the considerable improvement of drilling conditions [40]. In addition, a Vishay milling cutter (Vishay Precision Group, Malvern, PA, USA) was used for the drilling and producing holes with the final diameter of approximately 1.9 mm. The holes were drilled in incremental steps of 0.05 mm to a total depth of 1 mm. This study employed a three-element type-A [34] strain rosette gauge of FRS-2 (TML Lab. Company, Tokyo, Japan), paired with a multi-channel signal-acquisition device (P3 Strain Indicator and Recorder, Vishay Precision Group, Malvern, PA, USA) (with resolution of strain measurement equal to 10 −6 ). Four measurement points were located in the middle part of plate B3 and two on plate B4. The distance between the points varied from 30 to 70 mm. Additional residual stress estimation for the Zr 700 plate under the as-delivered condition was based on two measurement points.

Structural Properties
The process of explosive welding is characterized by the formation of an interface between the periodic deformation and the interfacial wave [3] (Figure 3a). The geometrical parameters of the wave depend on the process parameters and physical properties of the welded materials [7,[41][42][43]. These parameters could be correlated with mechanical properties of the composite structure [7,44,45]. For some welding systems, a melted area can be formed in the vortex of the collision zone. In this study, the following geometrical quantities were measured: wave height , wavelength , and melted area along the length of welded line . Figure 3b illustrates the measurement of the geometrical parameters of the samples cut out from both welded plates by using the digital optical method according. The total length of welded line varies between 15 and 18 mm, including 8-12 points for wavelength and wave height determination for the Zr 700-Ti Gr. 1 interface and 20-37 points for the Ti Gr. 1-P265GH interface. Analyzed data were collected to calculate the mean and standard deviation for each parameter. Following a previous study [7], the authors calculated a parameter that describes the averaged amount of melted area: equivalent melted thickness, = ⁄ . In addition to the geometrical properties, microhardness distribution was included as a structural property. The microhardness distribution provides information on induced material hardening due to severe plastic deformation that occurred during the impact of two plates. The distribution of Vickers microhardness (HV) under the 50-G load was measured along three lines perpendicular to interfaces with the distance of 0.06 mm between points in the vicinity of the welded zone. The final results were obtained as the mean values of the three measurements (three lines) supplemented with error bars representing standard deviations. The HV hardness of the as-delivered plates was also measured for comparison.

Mechanical Test
The tensile test was designed to verify the strength of the cross-section perpendicular to the interfaces. Figure 4 presents the geometry of the specimen used for the tensile test. The geometrical parameters of the wave depend on the process parameters and physical properties of the welded materials [7,[41][42][43]. These parameters could be correlated with mechanical properties of the composite structure [7,44,45]. For some welding systems, a melted area can be formed in the vortex of the collision zone. In this study, the following geometrical quantities were measured: wave height H, wavelength n, and melted area P along the length of welded line L. Figure 3b illustrates the measurement of the geometrical parameters of the samples cut out from both welded plates by using the digital optical method according. The total length of welded line L varies between 15 and 18 mm, including 8-12 points for wavelength and wave height determination for the Zr 700-Ti Gr. 1 interface and 20-37 points for the Ti Gr. 1-P265GH interface. Analyzed data were collected to calculate the mean and standard deviation for each parameter. Following a previous study [7], the authors calculated a parameter that describes the averaged amount of melted area: equivalent melted thickness, EMT = P/L.
In addition to the geometrical properties, microhardness distribution was included as a structural property. The microhardness distribution provides information on induced material hardening due to severe plastic deformation that occurred during the impact of two plates. The distribution of Vickers microhardness (HV) under the 50-G load was measured along three lines perpendicular to interfaces with the distance of 0.06 mm between points in the vicinity of the welded zone. The final results were obtained as the mean values of the three measurements (three lines) supplemented with error bars representing standard deviations. The HV hardness of the as-delivered plates was also measured for comparison.

Mechanical Test
The tensile test was designed to verify the strength of the cross-section perpendicular to the interfaces. Figure 4 presents the geometry of the specimen used for the tensile test. The test facilitated the determination of force 02 for the 0.2% offset of plastic strain, ultimate force , and elongation to rupture . The obtained values for plate B4 and its composite plates can be compared. These results can be verified using theoretical values calculated based on the mechanical properties of materials in the as-delivered condition.

Residual Stresses
The relieved strain components recorded during the incremental drilling were evaluated and recalculated with respect to residual principal stresses by using the Eval 7 software (Sint Technology). This software is fully compliant with the international ASTM E837-13a standard [34] for residual stress measurement using the hole-drilling strain-gage method. The software also allows evaluation of the uncertainty of stress calculation [46]. The following accuracies of material and drilling parameters were found: Young's modulus = ±3 GPa, Poisson ratio = ±0.01, strain = ±0.6 μm m ⁄ , strain gauge factor = ±1%, hole diameter = ±0.04 mm, and hole depth = ±0.025 mm. A uniform stress field was assumed throughout the calculations. The obtained maximum ( 1 ) and minimum ( 2 ) principal stresses may be considered as average values along the 1-mm hole depth, i.e., near the surface layer of Zr 700 plate. The results of the residual stresses determined in the Zr 700 layers of composite plates B3 and B4 as well as the reference stresses determined for the Zr 700 plate before welding are presented in Figure 5. The principal residual stresses determined for the as-delivered condition in the Zr 700 plate represent the state of the residual stress before welding (reference points in Figure 5). This biaxial The test facilitated the determination of force F p02 for the 0.2% offset of plastic strain, ultimate force F m , and elongation to rupture A. The obtained values for plate B4 and its composite plates can be compared. These results can be verified using theoretical values calculated based on the mechanical properties of materials in the as-delivered condition.

Residual Stresses
The relieved strain components recorded during the incremental drilling were evaluated and recalculated with respect to residual principal stresses by using the Eval 7 software (Sint Technology). This software is fully compliant with the international ASTM E837-13a standard [34] for residual stress measurement using the hole-drilling strain-gage method. The software also allows evaluation of the uncertainty of stress calculation [46]. The following accuracies of material and drilling parameters were found: Young's modulus = ±3 GPa, Poisson ratio = ±0.01, strain = ±0.6 µm/m, strain gauge factor = ±1%, hole diameter = ±0.04 mm, and hole depth = ±0.025 mm. A uniform stress field was assumed throughout the calculations. The obtained maximum (σ 1 ) and minimum (σ 2 ) principal stresses may be considered as average values along the 1-mm hole depth, i.e., near the surface layer of Zr 700 plate. The results of the residual stresses determined in the Zr 700 layers of composite plates B3 and B4 as well as the reference stresses determined for the Zr 700 plate before welding are presented in Figure 5.  The test facilitated the determination of force 02 for the 0.2% offset of plastic strain, ultimate force , and elongation to rupture . The obtained values for plate B4 and its composite plates can be compared. These results can be verified using theoretical values calculated based on the mechanical properties of materials in the as-delivered condition.

Residual Stresses
The relieved strain components recorded during the incremental drilling were evaluated and recalculated with respect to residual principal stresses by using the Eval 7 software (Sint Technology). This software is fully compliant with the international ASTM E837-13a standard [34] for residual stress measurement using the hole-drilling strain-gage method. The software also allows evaluation of the uncertainty of stress calculation [46]. The following accuracies of material and drilling parameters were found: Young's modulus = ±3 GPa, Poisson ratio = ±0.01, strain = ±0.6 μm m ⁄ , strain gauge factor = ±1%, hole diameter = ±0.04 mm, and hole depth = ±0.025 mm. A uniform stress field was assumed throughout the calculations. The obtained maximum ( 1 ) and minimum ( 2 ) principal stresses may be considered as average values along the 1-mm hole depth, i.e., near the surface layer of Zr 700 plate. The results of the residual stresses determined in the Zr 700 layers of composite plates B3 and B4 as well as the reference stresses determined for the Zr 700 plate before welding are presented in Figure 5. The principal residual stresses determined for the as-delivered condition in the Zr 700 plate represent the state of the residual stress before welding (reference points in Figure 5). This biaxial  The principal residual stresses determined for the as-delivered condition in the Zr 700 plate represent the state of the residual stress before welding (reference points in Figure 5). This biaxial compressive stress state with component values between −82 ± 8 MPa and −33 ± 4 MPa was transformed into the biaxial tensile stress state (10 ± 1 MPa and 76 ± 8 MPa) for composite plate B4. In contrast, composite plate B3, produced with a lower impact velocity of V p = 425 m/s as compared to plate B4 (V p = 468 m/s), indicated lower values of residual stresses, ranging between −35 ± 4 MPa and 20 ± 2 MPa. The performed manufacturing processes had a considerable effect on the residual stress state. The initial compressive stress state, which was beneficial in terms of stress-based corrosion cracking, became more tensile with the increasing magnitude of impact velocity. Figure 6 presents the morphologies of the interfacial waves for composite plates B3 and B4. As shown, the interfacial waves of the Zr 700-Ti Gr. 1 joint in both the plates did not exhibit melted areas (EMT = 0 µm) but showed higher values for the wavelength and wave height than those observed for the Ti Gr. 1-P265GH joint. The measured parameters are presented in Figure 7. Compared to plate B3, the higher impact velocity (by 10%) for plate B4 resulted in higher wavelength (by 31%) and wave height (by 14%) at the Zr 700-Ti Gr. 1 interface. At the Ti Gr. 1-P265GH interface, the wave parameters were nearly equal (within the standard deviation band). The EMT values were low [45], at approximately 3 and 5 µm for plates B3 and B4, respectively. In contrast, composite plate B3, produced with a lower impact velocity of = 425 m/s as compared to plate B4 ( = 468 m/s), indicated lower values of residual stresses, ranging between −35  4 MPa and 20  2 MPa. The performed manufacturing processes had a considerable effect on the residual stress state. The initial compressive stress state, which was beneficial in terms of stress-based corrosion cracking, became more tensile with the increasing magnitude of impact velocity. Figure 6 presents the morphologies of the interfacial waves for composite plates B3 and B4. As shown, the interfacial waves of the Zr 700-Ti Gr. 1 joint in both the plates did not exhibit melted areas ( = 0 μm) but showed higher values for the wavelength and wave height than those observed for the Ti Gr. 1-P265GH joint. The measured parameters are presented in Figure 7. Compared to plate B3, the higher impact velocity (by 10%) for plate B4 resulted in higher wavelength (by 31%) and wave height (by 14%) at the Zr 700-Ti Gr. 1 interface. At the Ti Gr. 1-P265GH interface, the wave parameters were nearly equal (within the standard deviation band). The values were low [45], at approximately 3 and 5 μm for plates B3 and B4, respectively.      The melted areas at the Ti Gr. 1-P265GH interface were localized mainly in the vortex formed as a result of fluid-structure interaction (Figure 8.). The melted areas comprise a new phase with mixed chemical composition of Ti and Fe (Figure 9). In both plates B3 and B4, multiple microcracks (Figures 8 and 9a) were detected in the melted areas; these were probably formed owing to severe residual stresses generated during the rapid cooling rate (shrinkage cracks [14]). Furthermore, grain deformation was observed to intensify closer to the weld line. The melted areas at the Ti Gr. 1-P265GH interface were localized mainly in the vortex formed as a result of fluid-structure interaction (Figure 8.). The melted areas comprise a new phase with mixed chemical composition of Ti and Fe (Figure 9). In both plates B3 and B4, multiple microcracks (Figures 8 and 9a) were detected in the melted areas; these were probably formed owing to severe residual stresses generated during the rapid cooling rate (shrinkage cracks [14]). Furthermore, grain deformation was observed to intensify closer to the weld line.  The microhardness distributions presented in Figure 10 exhibited an increase in the plate hardness in close vicinity of interfaces. In both plates B3 and B4, the distributions of microhardness were similar within the standard-deviation error bands. The highest value of microhardness of 250 HV0.05 was detected in the Ti Gr 1-P265GH interface; it exceeded the hardness of steel by approximately 40%. The melted areas at the Ti Gr. 1-P265GH interface were localized mainly in the vortex formed as a result of fluid-structure interaction (Figure 8.). The melted areas comprise a new phase with mixed chemical composition of Ti and Fe (Figure 9). In both plates B3 and B4, multiple microcracks (Figures 8 and 9a) were detected in the melted areas; these were probably formed owing to severe residual stresses generated during the rapid cooling rate (shrinkage cracks [14]). Furthermore, grain deformation was observed to intensify closer to the weld line.  The microhardness distributions presented in Figure 10 exhibited an increase in the plate hardness in close vicinity of interfaces. In both plates B3 and B4, the distributions of microhardness were similar within the standard-deviation error bands. The highest value of microhardness of 250 HV0.05 was detected in the Ti Gr 1-P265GH interface; it exceeded the hardness of steel by approximately 40%. The microhardness distributions presented in Figure 10 exhibited an increase in the plate hardness in close vicinity of interfaces. In both plates B3 and B4, the distributions of microhardness were similar within the standard-deviation error bands. The highest value of microhardness of 250 HV 0.05 was detected in the Ti Gr 1-P265GH interface; it exceeded the hardness of steel by approximately 40%.

Structural Properties
The microhardness distributions presented in Figure 10 exhibited an increase in the plate hardness in close vicinity of interfaces. In both plates B3 and B4, the distributions of microhardness were similar within the standard-deviation error bands. The highest value of microhardness of 250 HV0.05 was detected in the Ti Gr 1-P265GH interface; it exceeded the hardness of steel by approximately 40%.   Figure 11 presents the results of tensile tests represented as strain-force curves. The curves for the specimens made of composite plates B3 and B4 differ insignificantly.

Mechanical Test
The estimated curve parameters of yield force F p02 , ultimate force F m , elongation A, and equivalent Young's modulus E eq were calculated, as shown in Table 4. The equivalent Young's modulus was determined for the linear range of the curve as force F divided by total cross-section area A and strain ε, E eq = F/(Aε). Additionally, the fractures of both plates are presented in Figure 11.
Materials 2020, 13, x FOR PEER REVIEW 9 of 14 Figure 11 presents the results of tensile tests represented as strain-force curves. The curves for the specimens made of composite plates B3 and B4 differ insignificantly.

Mechanical Test
The estimated curve parameters of yield force 02 , ultimate force , elongation , and equivalent Young's modulus were calculated, as shown in Table 4. The equivalent Young's modulus was determined for the linear range of the curve as force divided by total cross-section area and strain , = /( ). Additionally, the fractures of both plates are presented in Figure  11.  The strain-force curve was estimated theoretically to quantify the obtained results with respect to the possible increase of strength properties [47] in relation to material properties in the as-delivered condition. The following assumptions were made in the calculation model: (i) the cross-section of the specimen (Figure 4) comprised uniform strain distribution and (ii) all the layers comprised the uniaxial stress state. This model applies constitutive empirical relations of − , − , and − of materials in the as-delivered condition (tensile tests). The recorded strain signal, , for the composite plate was used to estimate the stress in each layer through the following empirical  The strain-force curve was estimated theoretically to quantify the obtained results with respect to the possible increase of strength properties [47] in relation to material properties in the as-delivered condition. The following assumptions were made in the calculation model: (i) the cross-section of the specimen (Figure 4) comprised uniform strain distribution and (ii) all the layers comprised the uniaxial stress state. This model applies constitutive empirical relations of σ Zr − ε Zr , σ Ti − ε Ti , and σ St − ε St of materials in the as-delivered condition (tensile tests). The recorded strain signal, ε, for the composite plate was used to estimate the stress in each layer through the following empirical constitutive relations: σ Zr ε = ε Zr , σ Ti ε = ε Ti , and σ St ε = ε St . The stresses σ Zr , σ Ti , and σ St estimated through the force balance equation in each layer were used to determine force value F: where A Zr , A Ti , and A St are the initial cross-sectional areas of the Zr 700, Ti Gr 1, and P265GH layers, respectively. The empirical strain-stress curves for the material in the as-welded condition are presented in Figure 12a. The model implemented the initial cross-sectional areas, and thus its applicability was limited to a small strain regime (assumed to be less than 1%). The slope of the calculated curve in the linear range (up to~20 kN; Figure 12b) is in accordance with the slope of the experimental curves for both plates B3 and B4. Computed yield force F p02 = 25.7 kN was considerably lower than its empirical value of F p02 = 47.5 kN. The increase in the yield force by approximately 85% was due to material hardening in the vicinity of the interfaces. The research presented in [48][49][50] showed that the yield strength proportionally increased with the hardness of different types of steels and zirconium alloys [51]. The yield force F p02 of explosively welded plates is proposed to be predicted according to the proportional increase in yield stress R p02 as the function of hardness rate: where c i represents the proportionality factors for each layer (i = [Zr, Ti, St]), and r i HV = HV i h /HV i 0 represents the hardness rates (hardness of the hardened material HV i h divided by the hardness of the material in the initial state HV i 0 ). The hardness of HV i h was calculated as the average hardness of each layer (5 mm + 2 mm + 5 mm). The calculated hardness rates were as follows: r Zr HV = 0.97, r Ti HV = 1.16, and r St HV = 1.25. The proportionality factors were assumed to be equal, i.e., c Zr = c Ti = c St = c. Proportionality factor c = 1.58 was identified by fitting the experimental and calculated (Equation (2)) yield forces.
Materials 2020, 13, x FOR PEER REVIEW 10 of 14 value of 02 = 47.5 kN. The increase in the yield force by approximately 85% was due to material hardening in the vicinity of the interfaces. The research presented in [48][49][50] showed that the yield strength proportionally increased with the hardness of different types of steels and zirconium alloys [51]. The yield force 02 of explosively welded plates is proposed to be predicted according to the proportional increase in yield stress 02 as the function of hardness rate: where represents the proportionality factors for each layer ( = [ , , ]), and = ℎ 0 ⁄ represents the hardness rates (hardness of the hardened material ℎ divided by the hardness of the material in the initial state 0 ). The hardness of ℎ was calculated as the average hardness of each layer (5 mm + 2 mm + 5 mm). The calculated hardness rates were as follows: = 0.97, = 1.16, and = 1.25 . The proportionality factors were assumed to be equal, i.e., = = = . Proportionality factor = 1.58 was identified by fitting the experimental and calculated (Equation (2)) yield forces. The process of explosive welding includes problems of phase transformation, shock impact, plastic deformation, and fluid-structure interaction. A thorough analysis of the process requires sophisticated multiphysics numerical modeling [52][53][54][55], which is nowadays narrowed to the prediction of jet formation, morphology of the interfacial wave, and weldability. Residual stress formation has not yet been numerically simulated. However, based on the knowledge of the explosive welding process, a general scheme of residual stress generation can be proposed. During the shock of impact of the Zr 700 plate with the Ti Gr. 1 layer, a large hydrostatic compressive stress The process of explosive welding includes problems of phase transformation, shock impact, plastic deformation, and fluid-structure interaction. A thorough analysis of the process requires sophisticated multiphysics numerical modeling [52][53][54][55], which is nowadays narrowed to the prediction of jet formation, morphology of the interfacial wave, and weldability. Residual stress formation has not yet been numerically simulated. However, based on the knowledge of the explosive welding process, a general scheme of residual stress generation can be proposed. During the shock of impact of the Zr 700 plate with the Ti Gr. 1 layer, a large hydrostatic compressive stress due to inertial forces could be formed in the contact region. The increase of local temperature reduces yield stress of both materials in contact, allowing the occurrence of plastic deformation, which is sometimes manifested by the adiabatic shear bands [8,56,57]. More intensive, larger, and plastically deformed regions appear in a material with lower resistance to plastic yield. In most cases, the material with a lower yield strength and higher elongation is selected as the flyer. In this case, larger and more intensive plastic deformations occur in the flyer region in the vicinity of impact, and more elastic potential energy is stored in the base plate. When the pressure of explosive gas is released, the elastically deformed base plate below the interface expands and compresses the plastically deformed layer of the flyer plate. The induced compressive residual stresses in the vicinity of the interface must be balanced by the tensile residual stresses formed in the outer layer of the flyer plate (as a result of the spring-back effect [3]). The locally melted areas solidify and form a new phase; these areas are the sources of thermal residual stresses, which deviate from the general field of stresses described. The higher the differences in Young's modulus and thermal expansion coefficients, the higher the residual stresses. Stress relief with respect to heat treatment is possible only for materials with close values of thermal expansion coefficients.
In this study, the difference in the impact velocities by approximately 10% resulted in insignificant differences in microhardness distribution and tensile yield force of specimens with reduced thickness (5 mm + 2 mm + 5 mm). In addition, a notable increase of the wavelength by approximately 31% was observed. In contrast to most structural properties, the residual stresses in a 1-mm-thick Zr 700 surface layer exhibited profound sensitivity to the applied impact velocities. The initial compressive residual stress state was significantly transformed towards the tensile type, reaching 76 ± 8 MPa for higher impact velocities.

Conclusions
The main conclusions of the study are summarized as follows: • The compressive residual stress, which was initially present in the Zr 700 flyer plate, decreased in the explosive welding process, resulting in a tensile type with an increase in impact velocity.

•
To protect the composite plate from stress-based corrosion cracking, a lower value of the impact velocity is recommended.

•
The experimental yield force of composite specimens is around 85% higher than the yield force of combined properties of materials in the as-delivered condition.

•
The experimentally estimated residual stresses could be used to verify the numerical method applied in modeling of the explosive welding process.

•
In addition, a simple model based on microhardness measurement for yield force prediction of the composite plate was proposed. However, the model needs further verification.