Fig. 1 Representation of laser powder bed fusion process

Fig. 2 Defects during the fabrication: a warping and layer separation caused by high residual stress and b cracking in the part due to accumulated tensile stresses [50]. c Distortions and delamination during the AM process [42]. d Failure during manufacturing of a Ti-6Al-4V component caused by the build-up of residual stress [51]. e Example of a build that failed for a thin plate [36]

Fig. 3 Classification and formation mechanism of residual stress: a basic mechanisms of stress and plastic deformation development during: a heating and thermal expansion of new layer (top) and b cooling and thermal contraction of new layer (bottom) [63]. Cracks on the L-PBF part: c macro- and d microcracks [64]. e A schematic of different types of residual stress divided based on their crack length [63]. f Three different types of residual stress—type I, type II, and type III concerning their different crack spans: (1) Atom probe tomography analysis of hydrogen distribution in laser peened Ti6Al4V alloy: implications for residual stress evolution and hydrogen embrittlement control [65], (2) OIM grain boundary map with twin boundaries indicated by finer lines in Ni-base (alloy 600) stainless alloys [66], and (3) crack formation in a Ti6A14V thin wall produced via L-PBF caused by the build-up of residual stresses [51]

Fig. 4 Parameters of Bragg’s law in X-ray diffraction [75]

Fig. 5 The comparison of measurement methods in categories including penetration depth, cost, and accuracy—the methods are sorted from top to bottom [73,92,93]

Fig. 6 The schematic of essential process parameters mitigating residual stress, including laser power, scanning strategy, scanning speed, and hatch spacing

Fig. 7 The effect of the layer thickness on the dimension of the molten pool: a 25 μm layer thickness, b 50 μm layer thickness, and c 75 μm layer thickness of L-PBF fabrication of Ti-6Al-4V [127]

Fig. 8 a Various combinations of laser power and scanning speed considered for study; green squares indicate a combination giving high densification (> 99.9%) [132]. b Effect of varying the laser power on residual stress and cooling rate [127]. c Shear residual stress and d normal residual stress measured by XRD and hole-drilling residual stress measurements on the top surface of 12.7 mm L-PBF deposits fabricated with different scan speeds [133]

Fig. 9 Maximum von Mises stress at different laser power [134]: a schematic of the solution domain consisting of powder bed, b scanning strategy. Maximum von Mises stress at laser power 150 W and scanning speed 750 mm/s: c at the end of the first layer, d at the end of the second layer, e at the end of the third layer, and f at the end of the fifth layer. Maximum von Mises stress at laser power 120 W and scanning speed 750 mm/s: g at the end of the first layer and h at the end of the fifth layer [134]

Fig. 10 Effect of laser power on formation of residual stress for two different scanning strategies [135]: a schematic of the model used in FEA of L-PBF, b in-depth residual stress x-direction, and c in-depth residual stress in y-direction of the component [135]

Fig. 11 a Transient temperature distribution during layer melting at the end of the 5th track scan [140]. b Predicted melt pool temperature contours after scanning the 5th track [140]. c Melt pool width of various scanning speeds, and d melt pool depth of various scanning [140]. Numerical results showing the total molten powder volume (including both solidified and evaporated portions), the solidified molten volume, and the percentage of evaporated molten powder at different scanning speeds at laser power of e 150 W, f 250 W, g 350 W [141]

Fig. 12 Size of molten pool formed by L-PBF by two different scanning strategies [135]: a stripe scanning strategy and b chessboard (island) scanning strategy. Molten pool size in different L-PBF process parameters [135]: c P = 160 W, stripe scanning; d P = 160 W, chessboard scanning; e P = 200 W, stripe scanning; f P = 200 W, chessboard scanning. Effect laser power in-depth residual stress with different laser power of P = 160 W and P = 200 W, constant scanning speed and two scanning strategies [135]: g stripe scanning; h chessboard scanning

Fig. 13 Contour plot showing the optimal processing region of the laser process parameters for obtaining the best mechanical properties of Inconel 718 parts fabricated by L-PBF [155]

Fig. 14 The common scanning strategies used by researchers: a unidirectional, b un-unidirectional, c ° rotation, and d island scanning

Fig. 15 a Unidirectional scanning strategy. Profiles views of b von Mises stress, c surface normal stresses in y-direction, and d surface normal stresses in x-direction for 3 mm × 3 mm test case when using unidirectional scanning strategy. e Alternating scanning strategy. Profiles views of f von Mises stress, g surface normal stresses in y-direction, and h surface normal stresses in x-direction for 3 mm × 3 mm test case when using alternating scanning strategy. The schematic of scanning strategies used by Patterson [36]: i meander, j stripes. k Z-measurements from digital image correlation (DIC) along a diagonal of two test plates [36]. Different scanning strategies investigated by Peiying Bian [135]: l stripe of 0$^\circ$ and 30$^\circ$ rotation, m chessboard of 0$^\circ$ and 45$^\circ$

Fig. 16 Scanning strategies used in deposition and corresponding printed samples, von misses stress and stress analysis along different lines of the component [163]. Scanning strategies: a SDM, b RM, c SRM. Printed sample by scanning strategies: d SDM, e RM, f SRM. Contour of equivalent von mises stress for different scanning strategies: g SDM, h RM, i SRM. Residual stress distribution along line BC in different scanning strategies: j longitudinal stress, k transversal stress. l Normal stress distribution along line HI in different scanning strategies. m Longitudinal stress distribution along line DE in different scanning strategies. n Transversal stress distribution along line FG in different path strategies [163]

Fig. 17 Scanning strategies used by Cheng et al. [164] in the investigation of L-PBF fabrication of Inconel 718 and their corresponding temperature distribution, residual stress in y-direction, and residual stress in x-direction: a island scanning, b line scanning, c 45$^\circ$ line scanning, d 45$^\circ$ rotate scanning, e 90$^\circ$ rotate scanning, f 67$^\circ$ rotate scanning, g in–out scanning, h out-in scanning

Fig. 18 Twelve different scanning strategies that Zhang et al. used in [165]: a opposite S scanning, b parallel S 90$^\circ$ scanning, c parallel S no rotation scanning, d 0 approaching beam scanning, e 45$^\circ$ rotation approaching beam scanning, f opposite halves scanning, g parallel halves scanning, h island approaching beam scanning, i island mixed scanning, j beginning contour fill, k ending contour fill, and l delayed laser scanning. m The value of final average residual stress for each scanning strategy before releasing base plate constraints (S11, S22, and maximum principal stress) and n the value of final average residual stress for each scanning strategies releasing constraint (S11, S22, and maximum principal stress), and o the value of deflection in z-direction occurred in each scanning strategies after releasing base plate constraints [165]

Fig. 19 The scanning strategies and the relative longitudinal and transverse residual stress investigated by Zhan et al. [167]: a reciprocating scanning, b 90$^\circ$ reciprocating scanning, c line spacing, d screwing scanning, e reciprocating overlapping scanning, f island scanning

Fig. 20 Analyzing the effect of scanning strategy on residual stress by Zhang et al. [168], six scanning strategies and their corresponding experimental results of stresses in x-direction and y-direction are represented: a island scanning, b 0$^\circ$ no rotation, c 45$^\circ$ inclined 90$^\circ$ rotation, d 45$^\circ$ rotation, e 90$^\circ$ line rotation, f 67$^\circ$ rotation

Fig. 21 Scanning strategies and relative stress maps over the investigated mid-plane of the sample used by Strantza et al. [171] in L-PBF fabrication of Ti-6Al-4V: a schematic of the sample, b continuous, c island, d parallel, e island offset by 45°. Four scanning strategies and relative

Fig. 22 Von Mises equivalent stresses in the top surface for the sample tested by Nadammal et al. [178]: a the schematic of the sample, b X-, c Y-, d alternating, and e rotational strategy. The error is $\delta \sigma$ ≤ 50 MPa

Fig. 23 Representation of laser jumping [183]