Advancing quantitative description of porosity in autogenous laserwelds of 304L stainless steel
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Abstract
Porosity in linear autogenous laser welds of 304L stainless steel has been investigated using microcomputed tomography to reveal defect content in fiftyfour welds made with varying delivered power, travel speed and focal lens. Trends associated with porosity size and frequencies are shown and interfacial measures are employed to provide quantitative descriptors of pore shape, directionality, interspacing and solid linear fraction. Lastly, the coefficient of variation associated with equivalent pore radii is reported toward a discussion of microstructural variability and the influence of processparameters on such variability.
Keywords
Microcomputed tomography Porosity Stainless steel Interfacial shape distribution Interfacial normal distributionBackground
Among joining and metal processing techniques used in industrial and scientific capacities, laser welding is relatively new. Due to its ability to supply high densities of power to very controlled areas with minimal peripheral excess heat input, it has become a rapidly growing and highly attractive joining process for metals[1, 2]. Common interrogation practice for welds are often performed via postmortem failure analysis[3], postprocess radiography[4], or ultrasonic scan[5]. Typically, these evaluations provide an opportunity to identify the most probable cause of failure, or produce a qualitative understanding of the internal structure of the weld.
For most engineering metals, there exists a fairly clear inverse correlation between pore volume and mechanical properties such as strength or modulus with varying degrees of sensitivity. As a specific example, defects such as pores, occurring naturally or imposed artificially, have been shown to serve as preferred sites for the initiation or propagation of failure in creep in both conventional and high cycle fatigue of aluminum[6, 7], a material system having high formability and broad applications. 304L stainless steel is unique in this regard as the effects of porosity on some material properties challenge intuition. Two examples in the literature which illustrate this phenomena can be found in the work of Boyce et al.[3] and Kuo and Jeng[8]. In the work of Boyce et al., autogenous continuouswave and pulsedwave laser welds were made across the gauge section of 304L stainlesssteel tensile bars, which were subsequently strained to failure. While one weld schedule was noted to produce higher amounts of porosity than the other, no decrease in mechanical strength was observed. In the work of Kuo and Jeng, a variety of weld schedules were created for 304L stainless steel, where increasing porosity levels coincided with decreases in hardness and relatively small variations in yield strength. Additionally, the continuouswavelaser weld sample, which contained higher amounts of porosity than any pulsedwavelaser weld sample, demonstrated significantly higher tensile strength than all pulsedwavelaser weld samples[8]. These findings suggest that the interplay of processing parameters may affect laserwelded microstructure in ways that complicate the individual effect of porosity, particularly in 304L. Furthermore, both examples illustrate that the effects of laserwelding induced porosity in 304L on certain mechanical properties is not clearly understood. We suggest that advancing the quantitative description of porosity in 304L laser weldments and relating them directly to carefully controlled weld parameters can assist in better understanding the concomitant effects of porosity in this ubiquitous and highly damagetolerant material system.
Fortunately, for nearly all metallic systems, the parameters used to form the laserweld are among the most pivotal factors that determine the local microstructure. Typical processing parameters may include; shielding gas, laser power, power profile, filler material, travel speed and focal distance between the laser source and weld surface. The combination of these factors is often referred to as the ‘weld schedule’. In this study, parameters of the weld schedule investigated have been limited to weld power, travel speed and focal length. Fortunately, recent advances in characterization and microstructure visualization have provided a rich set of tools being increasingly brought to bear on laserweld induced porosity in a variety of metals[9, 10, 11, 12, 13]. The work presented here builds upon such investigations and utilizes microcomputed tomography and other emerging stateoftheart threedimensional (3D) characterization techniques to quantitatively relate porosity in autogenous laserwelds of 304L stainlesssteel to specific processing parameters[9, 10, 14].
Methods
Maximum pore volume and total pores observed per case
80 mm lens  

252 mm × min^{−1}  510 mm × min^{−1}  1016 mm × min^{−1}  1524 mm × min^{−1}  2032 mm × min^{−1}  
1200 W  0.49 mm^{3} (373)  0.05 mm^{3} (550)  0.03 mm^{3} (425)  
1000 W  0.76 mm^{3} (160)  0.30 mm^{3} (337)  0.03 mm^{3} (603)  0.02 mm^{3} (403)  
800 W  0.28 mm^{3} (60)  0.79 mm^{3} (190)  0.1 mm^{3} (612)  0.03 mm^{3} (835)  0.016 mm^{3} (349) 
600 W  0.17 mm^{3} (145)  0.38 mm^{3} (247)  0.045 mm^{3} (652)  0.013 mm^{3} (406)  0.008 mm^{3} (192) 
400 W  0.08 mm^{3} (394)  0.02 mm^{3} (343)  0.009 mm^{3} (116)  0.0005 mm^{3} (10)  0.0007 mm^{3} (20) 
200 W   (0)   (0)   (0)   (0)   (0) 
120 mm lens  
252 mm × min ^{ −1}  510 mm × min ^{ −1}  1016 mm × min ^{ −1}  1524 mm × min ^{ −1}  2032 mm × min ^{ −1}  
1200 W  0.95 mm^{3} (431)  0.10 mm^{3} (391)  0.03 mm^{3} (736)  
1000 W  1.50 mm^{3} (130)  0.51 mm^{3} (190)  0.57 mm^{3} (381)  0.01 mm^{3} (263)  
800 W  0.17 mm^{3} (77)  0.59 mm^{3} (129)  0.09 mm^{3} (302)  0.01 mm^{3} (290)  0.006 mm^{3} (264) 
600 W  0.24 mm^{3} (120)  0.26 mm^{3} (284)  0.01 mm^{3} (267)  0.007 mm^{3} (132)  0.009 mm^{3} (91) 
400 W  0.07 mm^{3} (81)  0.01 mm^{3} (6)  0.001 mm^{3} (1)   (0)   (0) 
200 W   (0)   (0)   (0)   (0)   (0) 
Characterization
Pore characterization
Utilizing the reconstructions obtained and the known voxel resolutions for each weld sample, physical measures of pore size, population and frequency were calculated for pores constituting ninetypercent or more of the voided space within each sample. These values serve as a baseline and comparison for readily employed measures of pore presence.
Interfacial morphology
Interfacial orientation
The interfacial normal$\left(\widehat{\mathit{n}}\right)$ associated with each interfacial patch of a dataset is used to define a probability distribution for their orientation in threedimensional space. The method used to visualize this probability distribution is the Interfacial Normal Distribution or IND[23, 24]. In this visualization technique, the twodimensional projection of a sphere with respect to a given axis displays the probability of occurrence of a given normal orientation. In this study, all INDs are presented as projections along the positive zaxis, which is also the direction of travel for the workpiece beneath the welding laser. Thus, the upper and lower hemispheres correspond to the direction toward and away from the laser, respectively. The color values at each location in the IND indicate the probability of encountering a particular normal based on the population of normals within the dataset. The color bar associated with each IND presented later in the section on results represents nondimensional probability.
Spatial analysis
When the isodistance structures join together from thresholding with a negative threshold value, a change in the number of voids arises. This occurs at a distance value corresponding to half of the pore interspacing (the distance between interfaces at the narrowest point). Since we are examining systems that contain a variety of spatial distributions of pores, PIDs are calculated by measuring the rate at which pores are joining as a function of the distance threshold. Specifically, the PID is calculated by taking the negative derivative (−1 times the derivative) of the number of voids as a function of twice the distance threshold. Numerically, a central differencing method is used to calculate the derivatives. Each point in the PID represents the probability of finding a pair of pores with the pore interspacing at the corresponding distance threshold value. Furthermore, a characteristic pore interspacing is calculated by taking the weighted mean of the pore interspacing.
where R is one half of the characteristic pore interspacing and r is the characteristic pore radius. The SLF provides a measure of local linear fraction of solid along the path connecting the center of the particles and passing through the narrowest matrix region. Unlike pore volume fraction, another commonly used measure of density, the SLF does not depend on the volume used for the calculation. This is of particular note for each weld schedule studied here, as laser weld porosity is generally a localized phenomena often occurring at the centerline of the weld and not distributed homogeneously throughout the weld. Furthermore, the SLF is useful as it yields a quantitative metric of solid material between regions of densely populated pores relative to the size of pores present. It is expected that this type of spacing sensitivity metric would have a strong influence on the mechanical properties of the weld.
Results and discussion
Population statistics
Interfacial shape distributions
The curvature distributions for a given travel speed are rather consistent across all power levels. The primary difference in ISDs relating to power variation, see Additional file3,4 is that the peak of the curvature distributions exist at increasingly negative values of κ_{2} with decreases in power. This change corresponds to more spherical pore morphologies being formed with decreases in weld power. These trends were observed consistently across both focal length welds. A full set of calculated ISDs for all weld cases in this study having more than twenty pores each are included in the Additional file3,4 to this article.
Interfacial normal distributions
Pore interspacing
Pore interspacing, radius and SLF as functions of weld power and speed
80 mm lens  120 mm lens  

Weld power (W)  Pore interspacing (μm)  Pore radius (μm)  SLF  Pore interspacing (μm)  Pore radius (μm)  SLF 
400  300 (14.8)  51 (7.4)  0.75 (0.05)       
600  124 (9.1)  52 (4.6)  0.54 (0.05)  78 (9)  41 (4.5)  0.49 (0.07) 
800  144 (9.2)  69 (4.6)  0.51 (0.04)  107 (9)  88 (4.5)  0.38 (0.04) 
1000  170 (14.2)  82 (7.1)  0.51 (0.05)  110 (14.6)  104 (7.8)  0.35 (0.05) 
1200  240 (15.5)  89 (7.8)  0.58 (0.05)  210 (20)  120 (10)  0.47 (0.05) 
Weld speed (mm × min ^{ −1} )  Pore interspacing (μm)  Pore radius (μm)  SLF  Pore interspacing (μm)  Pore radius (μm)  SLF 
252  270 (14.8)  108 (7.4)  0.55 (0.04)  340 (14.6)  129 (7.8)  0.57 (0.04) 
510  170 (14.8)  142 (7.4)  0.37 (0.04)  160 (14.6)  124 (7.8)  0.40 (0.04) 
1016  124 (9.1)  52 (4.5)  0.54 (0.05)  78 (9)  41 (4.5)  0.49 (0.07) 
1524  110 (14.3)  63 (7.1)  0.47 (0.07)  230 (14.6)  51 (7.8)  0.70 (0.06) 
2032  190 (14.3)  57 (7.1)  0.62 (0.06)  310 (14.6)  58 (7.8)  0.72 (0.05) 
Pore interspacing was also calculated for various weld speeds, as shown in Figure 10. Again, to reduce redundancy and to make the trend clear, only select results are shown for welds made at multiple speeds in conjunction with the 120 mm focal length at 600 W. While the probability of finding pores at interspacing distances below 250 microns is relatively high across all cases, the distributions appear to be broader for low and high travel speeds, with the high travelspeed case potentially exhibiting a bimodal distribution. However, the statistics are insufficient to conclusively determine whether a bimodal distribution exists; further examination of larger weld samples or a larger number of samples under the same processing parameters are required to do so.
As described earlier, pore interspacing is a measure of the proximity of pores in the weld structure, while the SLF measures the proximity of pores relative to the distance between their centers and the characteristic pore size. For the samples where weld power is varied, the smallest pore interspacing was found at 600 W for a speed of 1016 mm × min^{−1} for both 80 and 120 mm lens welds (see Table 2), while the minimum SLF occurs at weld powers of 800 – 1000 W for the same travel speed (Figure 11a). This is consistent with the results of Figure 6, where the structure with the highest pore frequency per unit length arises at a weld power of 800 W for the 1016 mm × min^{−1} speed weld series. While these results are consistent, SLF provides a more insightful detail of the pore structures present; for example, in the case of 800 W welds formed at 1016 mm × min^{−1} with a 120 mm focus lens, the pore interfaces are separated by a distance that is 0.39 times the centertocenter distance between neighboring pores on average. Additionally, it is valuable to point out that the SLF is in the range of 0.4 to 0.6 for welds with a broad range of process parameters, which indicates that characteristic pore interspacing is approximately the same as the characteristic pore diameter in these cases. This suggests that for many weld cases, the characteristic pore interspacing can be approximated by the average pore diameter, which is generally easier to measure. However, high SLF values (> 0.6) are observed at the lowest power and the highest speed, indicating that pores may be spaced farther apart relative to their size at low delivered energy (Table 2 and Figure 11).
Pore size variability
Conclusions
In this paper, quantitative characterization of porosity in laserwelds of 304L stainless steel has been performed nondestructively for 54 unique continuouswave weld schedules via microcomputed tomography where each weld schedule represents a unique dataset. Direct correlations of pore size, shape, frequency, directionality, pore interspacing and solid linear fraction (SLF) with weld processing parameters have been made.
We find:

Average and maximum pore volume increase with decreasing speed or increasing power.

Pore frequency initially increases and then decreases with increasing power for a given travel speed.

Interfacial shape distributions (ISDs) and interfacial normal distributions (INDs) illustrate that basic pore shape and directionality are similar for a given welding speed regardless of power delivered.

ISDs show that pore shapes are nearly spherical or ellipsoidal at low and high travel speeds and are far more irregular, with a mix of ellipsoidal and saddleshape geometries at moderate travel speeds.

INDs indicate that pore orientations become anisotropic at moderate to high travel speeds with large concentrations of pore interfacial normals pointing toward and away from the direction of laser incidence.

Characteristic pore interspacing is nominally equivalent to characteristic pore diameter for welds with a broad range of process parameters, as reflected in the solid linear fraction (SLF) values.

The values of c.v. indicate that the spread in pore radii is small with respect to their mean value for all weld schedules.

High travel speeds and low delivered power result in the lowest pore linear frequency while increasing the amount of solid material between pores, which would likely yield improved mechanical properties.
Availability of supporting data
Animations of the five primary 3D reconstructions featured in this article for which ISDs, INDs, pore interspacing and SLF were calculated and presented have been made publicly available[27].
Notes
Acknowledgements
Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy’s National Nuclear Security Administration under contract DEAC0494AL85000. V.W.L. Chan and K. Thornton would like to acknowledge NSF DMR Grant # 0746424 “CAREER: Integrated Research and Education Program in ThreeDimensional Materials Science and Visualization.” The computational resources for calculations of pore interspacing and pore sizes were provided by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI1053575, under allocation No. TGDMR110007.
Supplementary material
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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.