Advancing quantitative description of porosity in autogenous laser-welds of 304L stainless steel
© Madison et al.; licensee Springer. 2014
Received: 11 November 2013
Accepted: 21 March 2014
Published: 29 April 2014
Porosity in linear autogenous laser welds of 304L stainless steel has been investigated using micro-computed tomography to reveal defect content in fifty-four 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 process-parameters on such variability.
KeywordsMicro-computed tomography Porosity Stainless steel Interfacial shape distribution Interfacial normal distribution
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 post-mortem failure analysis, post-process radiography, or ultrasonic scan. 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. and Kuo and Jeng. In the work of Boyce et al., autogenous continuous-wave and pulsed-wave laser welds were made across the gauge section of 304L stainless-steel 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 continuous-wave-laser weld sample, which contained higher amounts of porosity than any pulsed-wave-laser weld sample, demonstrated significantly higher tensile strength than all pulsed-wave-laser weld samples. These findings suggest that the interplay of processing parameters may affect laser-welded microstructure in ways that complicate the individual effect of porosity, particularly in 304L. Furthermore, both examples illustrate that the effects of laser-welding 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 damage-tolerant material system.
Fortunately, for nearly all metallic systems, the parameters used to form the laser-weld 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 laser-weld induced porosity in a variety of metals[9–13]. The work presented here builds upon such investigations and utilizes micro-computed tomography and other emerging state-of-the-art three-dimensional (3D) characterization techniques to quantitatively relate porosity in autogenous laser-welds of 304L stainless-steel to specific processing parameters[9, 10, 14].
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
0.49 mm3 (373)
0.05 mm3 (550)
0.03 mm3 (425)
0.76 mm3 (160)
0.30 mm3 (337)
0.03 mm3 (603)
0.02 mm3 (403)
0.28 mm3 (60)
0.79 mm3 (190)
0.1 mm3 (612)
0.03 mm3 (835)
0.016 mm3 (349)
0.17 mm3 (145)
0.38 mm3 (247)
0.045 mm3 (652)
0.013 mm3 (406)
0.008 mm3 (192)
0.08 mm3 (394)
0.02 mm3 (343)
0.009 mm3 (116)
0.0005 mm3 (10)
0.0007 mm3 (20)
120 mm lens
252 mm × min −1
510 mm × min −1
1016 mm × min −1
1524 mm × min −1
2032 mm × min −1
0.95 mm3 (431)
0.10 mm3 (391)
0.03 mm3 (736)
1.50 mm3 (130)
0.51 mm3 (190)
0.57 mm3 (381)
0.01 mm3 (263)
0.17 mm3 (77)
0.59 mm3 (129)
0.09 mm3 (302)
0.01 mm3 (290)
0.006 mm3 (264)
0.24 mm3 (120)
0.26 mm3 (284)
0.01 mm3 (267)
0.007 mm3 (132)
0.009 mm3 (91)
0.07 mm3 (81)
0.01 mm3 (6)
0.001 mm3 (1)
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 ninety-percent or more of the voided space within each sample. These values serve as a baseline and comparison for readily employed measures of pore presence.
The interfacial normal associated with each interfacial patch of a dataset is used to define a probability distribution for their orientation in three-dimensional space. The method used to visualize this probability distribution is the Interfacial Normal Distribution or IND[23, 24]. In this visualization technique, the two-dimensional 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 z-axis, which is also the direction of travel for the work-piece 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 non-dimensional probability.
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
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 κ2 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, 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)
Pore interspacing (μm)
Pore radius (μm)
Weld speed (mm × min −1 )
Pore interspacing (μm)
Pore radius (μm)
Pore interspacing (μm)
Pore radius (μm)
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 travel-speed 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 center-to-center 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
In this paper, quantitative characterization of porosity in laser-welds of 304L stainless steel has been performed non-destructively for 54 unique continuous-wave weld schedules via micro-computed 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.
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 saddle-shape 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.
Sandia National Laboratories is a multi-program 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 DE-AC04-94AL85000. V.W.L. Chan and K. Thornton would like to acknowledge NSF DMR Grant # 0746424 “CAREER: Integrated Research and Education Program in Three-Dimensional 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 OCI-1053575, under allocation No. TG-DMR110007.
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