1._CRD Introduction_NN1 
A_AT0 major_AJ0 area_NN1 of_PRF focus_NN1 in_PRP the_AT0 field_NN1 of_PRF additive_AJ0 manufacturing_NN1 (_PUL AM_AV0 )_PUR is_VBZ understanding_VVG pore_NN1 formation_NN1 ,_PUN and_CJC process_NN1 optimization_NN1 with_PRP the_AT0 goal_NN1 of_PRF creating_VVG fully_AV0 dense_AJ0 ,_PUN defect-free_AJ0 components_NN2 ._SENT Studying_VVG the_AT0 effect_NN1 of_PRF pores_NN2 on_PRP metal_NN1 failure_NN1 ,_PUN along_AVP with_PRP the_AT0 development_NN1 of_PRF failure_NN1 models_NN2 based_VVN on_PRP theory_NN1 and_CJC experiments_NN2 has_VHZ a_AT0 long_AJ0 and_CJC continued_AJ0 history_NN1 for_PRP conventionally_AV0 processed_AJ0 ductile_AJ0 metals_NN2 due_AJ0 to_PRP the_AT0 importance_NN1 of_PRF avoiding_VVG failure_NN1 in_PRP load_NN1 bearing_VVG components_NN2 or_CJC during_PRP metal_NN1 forming_VVG ._SENT For_PRP example_NN1 ,_PUN in_PRP 1977_CRD Gurson_NP0 developed_VVD a_AT0 model_NN1 in_PRP terms_NN2 of_PRF a_AT0 yield_NN1 function_NN1 and_CJC microstructurally_AV0 informed_VVN void_AJ0 volume_NN1 fraction_NN1 to_TO0 understand_VVI void_AJ0 growth_NN1 and_CJC ductile_AJ0 failure_NN1 using_VVG simplified_AJ0 spherical_AJ0 and_CJC cylindrical_AJ0 void_AJ0 models_NN2 ._SENT By_PRP combining_VVG the_AT0 existing_AJ0 frameworks_NN2 for_PRP fracture_NN1 modeling_NN1 with_PRP the_AT0 unique_AJ0 manufacturing_NN1 capabilities_NN2 of_PRF AM_NP0 ,_PUN new_AJ0 insight_NN1 into_PRP the_AT0 effect_NN1 of_PRF pores_NN2 on_PRP ductile_AJ0 failure_NN1 is_VBZ possible_AJ0 ._SENT 
Laser_NN1 powder_NN1 bed_NN1 fusion_NN1 (_PUL L-PBF_NP0 )_PUR AM_AV0 is_VBZ a_AT0 process_NN1 for_PRP building_VVG metallic_AJ0 components_NN2 layer-by-layer_NN1 using_VVG a_AT0 focused_AJ0 laser_NN1 heat_NN1 source_NN1 to_TO0 melt_VVI a_AT0 selected_AJ0 2-dimensional_AJ0 pattern_NN1 in_PRP a_AT0 thin_AJ0 layer_NN1 (_PUL 10_CRD –_PUN 100_CRD µm_NN0 )_PUR of_PRF powder_NN1 feedstock_NN1 to_PRP a_AT0 baseplate_NN1 ,_PUN lowering_VVG the_AT0 baseplate_NN1 by_PRP a_AT0 prescribed_AJ0 layer_NN1 thickness_NN1 ,_PUN spreading_VVG on_PRP a_AT0 new_AJ0 layer_NN1 ,_PUN scanning_VVG the_AT0 next_ORD layer_NN1 pattern_NN1 ,_PUN which_DTQ fuses_VVZ to_PRP the_AT0 previous_AJ0 layer_NN1 ,_PUN and_CJC repeating_VVG until_PRP a_AT0 final_AJ0 3-dimensional_AJ0 (_PUL 3D_NN0 )_PUR component_NN1 is_VBZ completed_VVN ._SENT In_PRP AM_AV0 ,_PUN there_EX0 are_VBB numerous_AJ0 processing_NN1 parameters_NN2 that_CJT dictate_VVB a_AT0 completed_AJ0 component_NN1 's_POS quality_NN1 ._SENT One_CRD primary_AJ0 evaluation_NN1 metric_AJ0 for_PRP optimizing_VVG a_AT0 parameter_NN1 set_VVN for_PRP a_AT0 given_AJ0 alloy_NN1 is_VBZ component_AJ0 density_NN1 ,_PUN or_CJC the_AT0 reduction_NN1 of_PRF pores_NN2 ._SENT Pores_NN2 in_PRP AM_AV0 parts_NN2 can_VM0 be_VBI formed_VVN via_PRP different_AJ0 mechanisms_NN2 ;_PUN two_CRD of_PRF the_AT0 primary_AJ0 mechanisms_NN2 are_VBB :_PUN (_PUL 1_CRD )_PUR gas_NN1 entrapment_NN1 during_PRP melting_NN1 and_CJC solidification_NN1 of_PRF the_AT0 meltpools_NN2 ,_PUN analogous_AJ0 to_PRP that_DT0 seen_VVN in_PRP casting_NN1 and_CJC welding_NN1 ,_PUN which_DTQ generates_VVZ spherical_AJ0 pores_NN2 and_CJC (_PUL 2_CRD )_PUR irregular_AJ0 morphology_NN1 lack-of-fusion_NN1 (_PUL LoF_NP0 )_PUR pores_NN2 ,_PUN which_DTQ are_VBB formed_VVN due_AJ0 to_PRP incomplete_AJ0 fusion_NN1 between_PRP layers_NN2 or_CJC adjacent_AJ0 meltpools_NN2 on_PRP the_AT0 same_DT0 layer_NN1 along_PRP the_AT0 heat_NN1 source_NN1 scanning_NN1 path_NN1 ,_PUN and_CJC which_DTQ can_VM0 have_VHI sharp_AJ0 features_NN2 ._SENT LoF_AJ0 pores_NN2 are_VBB of_PRF primary_AJ0 interest_NN1 in_PRP AM_AV0 because_CJS of_PRF their_DPS significantly_AV0 more_AV0 detrimental_AJ0 influence_NN1 on_PRP material_NN1 ductility_NN1 compared_VVN to_PRP spherical_AJ0 pores_NN2 ._SENT 
In_PRP addition_NN1 to_PRP pores_NN2 having_VHG a_AT0 harmful_AJ0 effect_NN1 on_PRP the_AT0 fracture_NN1 behavior_NN1 of_PRF ductile_AJ0 metals_NN2 ,_PUN stress_NN1 state_NN1 is_VBZ also_AV0 known_VVN to_TO0 play_VVI an_AT0 important_AJ0 role_NN1 in_PRP fracture_NN1 ._SENT Stress_NN1 state_NN1 can_VM0 be_VBI defined_VVN using_VVG the_AT0 two_CRD parameters_NN2 stress_NN1 triaxiality_NN1 (_PUL η_NP0 )_PUR and_CJC Lode_NP0 angle_NN1 parameter_NN1 (_PUL θ¯_NP0 )_PUR ._SENT The_AT0 stress_NN1 triaxiality_NN1 is_VBZ the_AT0 ratio_NN1 of_PRF the_AT0 mean_AJ0 stress_NN1 (_PUL σm_NN1 )_PUR and_CJC von_NP0 Mises_VVZ equivalent_AJ0 stress_NN1 (_PUL σ¯VM_NP0 )_PUR :_PUN equation_NN1 (_PUL 1_CRD )_PUR where_AVQ I1_AJ0 =_NP0 σkk_NP0 is_VBZ the_AT0 first_ORD invariant_AJ0 of_PRF the_AT0 stress_NN1 tensor_NN1 ,_PUN σ_NN1 ,_PUN and_CJC J2_CRD =_NP0 1_CRD /_PUN 2sijsij_NP0 is_VBZ the_AT0 second_ORD invariant_AJ0 of_PRF the_AT0 deviatoric_AJ0 stress_NN1 tensor_NN1 ,_PUN s._NN0 The_AT0 normalized_AJ0 Lode_NN1 angle_NN1 parameter_NN1 is_VBZ a_AT0 function_NN1 of_PRF the_AT0 third_ORD invariant_AJ0 of_PRF the_AT0 deviatoric_AJ0 stress_NN1 tensor_NN1 ,_PUN J3_NP0 =_NP0 det_NN1 (_PUL sij_NP0 )_PUR ,_PUN and_CJC is_VBZ defined_VVN as_PRP :_PUN equation_NN1 (_PUL 2_CRD )_PUR ._SENT 
Increased_AJ0 stress_NN1 triaxiality_NN1 is_VBZ known_VVN to_TO0 accelerate_VVI the_AT0 void_AJ0 nucleation_NN1 and_CJC growth_NN1 process_NN1 in_PRP ductile_AJ0 metals_NN2 ,_PUN resulting_VVG in_PRP reduced_AJ0 ductility_NN1 even_AV0 in_PRP fully_AV0 dense_AJ0 samples_NN2 ._SENT Designing_VVG load_NN1 bearing_VVG components_NN2 to_TO0 be_VBI safe_AJ0 under_PRP the_AT0 spatially_AV0 varying_AJ0 stress_NN1 state_NN1 is_VBZ an_AT0 important_AJ0 consideration_NN1 for_PRP engineers_NN2 in_PRP the_AT0 design_NN1 against_PRP failure_NN1 ._SENT 
Fracture_NN1 models_NN2 that_CJT describe_VVB the_AT0 effects_NN2 of_PRF stress_NN1 state_NN1 on_PRP ductile_AJ0 failure_NN1 have_VHB primarily_AV0 been_VBN presented_VVN in_PRP mixed_AJ0 stress-strain_AJ0 space_NN1 ,_PUN meaning_VVG equivalent_AJ0 plastic_NN1 strain_NN1 to_PRP failure_NN1 versus_PRP η_NP0 and_CJC θ¯_NP0 (_PUL referred_VVN to_PRP here_AV0 as_CJS equivalent_AJ0 strain_NN1 space_NN1 )_PUR because_CJS in_PRP ductile_AJ0 fracture_NN1 ,_PUN the_AT0 resolution_NN1 in_PRP strain_NN1 is_VBZ typically_AV0 much_AV0 larger_AJC than_CJS the_AT0 resolution_NN1 in_PRP stress_NN1 ,_PUN that_DT0 is_VBZ ,_PUN large_AJ0 differences_NN2 in_PRP strain_NN1 result_NN1 in_PRP relatively_AV0 minor_AJ0 differences_NN2 in_PRP stress_NN1 due_AJ0 to_PRP the_AT0 fact_NN1 that_CJT the_AT0 elastic_AJ0 contribution_NN1 to_PRP failure_NN1 is_VBZ negligible_AJ0 compared_VVN to_PRP the_AT0 plastic_NN1 contribution_NN1 ._SENT However_AV0 ,_PUN for_PRP alloys_NN2 with_PRP little_DT0 to_PRP no_AT0 plastic_NN1 deformation_NN1 to_PRP failure_NN1 ,_PUN describing_VVG failure_NN1 in_PRP terms_NN2 of_PRF strain_NN1 to_PRP failure_NN1 becomes_VVZ more_AV0 challenging_AJ0 ._SENT This_DT0 is_VBZ shown_VVN schematically_AV0 in_PRP Figure_NN1 1_CRD ,_PUN which_DTQ compares_VVZ the_AT0 engineering_NN1 stress-strain_AJ0 curves_NN2 for_PRP the_AT0 two_CRD materials_NN2 in_PRP this_DT0 study_NN1 —_PUN Ti-6Al-4V_NP0 and_CJC 316L_NP0 stainless_AJ0 steel_NN1 (_PUL 316L_NP0 )_PUR ._SENT 
In_PRP this_DT0 study_NN1 ,_PUN the_AT0 effect_NN1 of_PRF pores_NN2 relative_AJ0 to_PRP the_AT0 behavior_NN1 of_PRF dense_AJ0 samples_NN2 was_VBD assessed_VVN in_PRP two_CRD different_AJ0 alloys_NN2 using_VVG well-known_AJ0 fracture_NN1 models_NN2 calibrated_VVN in_PRP both_DT0 equivalent_AJ0 stress_NN1 and_CJC strain_NN1 space_NN1 ._SENT Data_NN0 over_PRP a_AT0 wide_AJ0 range_NN1 of_PRF stress_NN1 states_NN2 from_PRP previous_AJ0 studies_NN2 by_PRP the_AT0 authors_NN2 on_PRP L-PBF_AJ0 stainless_AJ0 steel_NN1 316L_NP0 and_CJC L-PBF_NP0 Ti-6Al-4V_NP0 that_CJT included_VVD intentionally_AV0 manufactured_AJ0 ,_PUN penny-shaped_AJ0 pores_NN2 of_PRF varying_AJ0 diameter_NN1 were_VBD used_VVN to_TO0 calibrate_VVI fracture_NN1 models_NN2 for_PRP each_DT0 pore_NN1 size_NN1 in_PRP stress_NN1 triaxiality_NN1 versus_PRP Lode_NP0 angle_NN1 parameter_NN1 versus_PRP equivalent_AJ0 stress_NN1 space_NN1 (_PUL Haigh-Westergaard_NP0 space_NN1 ,_PUN referred_VVN to_PRP here_AV0 as_CJS equivalent_AJ0 stress_NN1 space_NN1 )_PUR and_CJC equivalent_AJ0 strain_NN1 space_NN1 ._SENT By_PRP comparing_VVG the_AT0 ductile_AJ0 316L_AJ0 alloy_NN1 (_PUL >_NN1 60_CRD %_NN0 engineering_NN1 strain_NN1 to_PRP failure_NN1 under_PRP uniaxial_AJ0 tension_NN1 )_PUR to_PRP the_AT0 less_AV0 ductile_AJ0 Ti-6Al-4V_NP0 (_PUL <_NN1 10_CRD %_NN0 engineering_NN1 strain_NN1 to_PRP failure_NN1 under_PRP uniaxial_AJ0 tension_NN1 )_PUR in_PRP both_DT0 equivalent_AJ0 stress_NN1 and_CJC strain_NN1 space_NN1 as_PRP a_AT0 function_NN1 of_PRF pore_NN1 size_NN1 ,_PUN an_AT0 assessment_NN1 of_PRF dominant_AJ0 fracture_NN1 mechanism_NN1 changes_NN2 ,_PUN if_CJS any_DT0 ,_PUN can_VM0 be_VBI made_VVN for_PRP each_DT0 material_NN1 ._SENT Additionally_AV0 ,_PUN the_AT0 appropriateness_NN1 of_PRF fracture_NN1 models_NN2 in_PRP equivalent_AJ0 stress_NN1 space_NN1 versus_PRP equivalent_AJ0 plastic_NN1 strain_NN1 space_NN1 for_PRP capturing_VVG the_AT0 effect_NN1 of_PRF pore_NN1 size_NN1 on_PRP the_AT0 failure_NN1 behavior_NN1 of_PRF both_DT0 materials_NN2 is_VBZ discussed_VVN ._SENT 
2._CRD Materials_NN2 and_CJC Methods_NN2 
The_AT0 complete_AJ0 description_NN1 of_PRF the_AT0 manufacturing_NN1 process_NN1 ,_PUN samples_NN2 ,_PUN experimental_AJ0 set-up_NN1 ,_PUN and_CJC simulations_NN2 are_VBB described_VVN in_PRP extensive_AJ0 detail_NN1 for_PRP the_AT0 316L_NN1 builds_VVZ in_PRP Refs_NN2 ._SENT and_CJC for_PRP the_AT0 Ti-6Al-4V_NP0 builds_VVZ in_PRP Refs_NN2 ._SENT ._SENT The_AT0 following_AJ0 is_VBZ an_AT0 overview_NN1 of_PRF information_NN1 that_DT0 is_VBZ most_AV0 pertinent_AJ0 to_PRP the_AT0 current_AJ0 study_NN1 ._SENT 
2.1_CRD ._SENT Experimental_AJ0 Methods_NN2 
Samples_NN2 used_VVN in_PRP this_DT0 study_NN1 for_PRP both_DT0 alloys_NN2 were_VBD manufactured_VVN on_PRP a_AT0 3DSystems_NN2 ,_PUN Inc._AJ0 ProX_NN1 320_CRD L-PBF_NP0 AM_NP0 machine_NN1 (_PUL 3DSystems_NN2 ,_PUN Rock_NP0 Hill_NP0 ,_PUN SC_NN0 ,_PUN USA_NP0 )_PUR ._SENT No_AT0 post-processing_AJ0 heat_NN1 treatment_NN1 was_VBD used_VVN for_PRP the_AT0 316L_NP0 builds_VVZ ,_PUN while_CJS a_AT0 post-processing_AJ0 stress_NN1 relief_NN1 heat_NN1 treatment_NN1 of_PRF 650_CRD °_NN0 C_ZZ0 for_PRP 3_CRD h_ZZ0 in_PRP an_AT0 argon_NN1 environment_NN1 was_VBD used_VVN for_PRP the_AT0 Ti-6Al-4V_NP0 builds_VVZ ._SENT Data_NN0 obtained_VVD using_VVG five_CRD different_AJ0 sample_NN1 geometries_NN2 ,_PUN selected_VVN as_CJS they_PNP have_VHB a_AT0 pre-determined_AJ0 failure_NN1 initiation_NN1 location_NN1 ,_PUN and_CJC corresponding_VVG to_PRP five_CRD unique_AJ0 stress_NN1 states_NN2 ,_PUN were_VBD used_VVN in_PRP the_AT0 current_AJ0 study_NN1 :_PUN pure_AJ0 shear_VVB ,_PUN equibiaxial_AJ0 tension_NN1 (_PUL punch_VVB tests_NN2 )_PUR ,_PUN and_CJC round_PRP notched_AJ0 tension_NN1 with_PRP three_CRD different_AJ0 notch_NN1 radii_NN2 (_PUL 3_CRD mm_NN0 (_PUL R3_CRD )_PUR ,_PUN 5_CRD mm_NN0 (_PUL R5_CRD )_PUR ,_PUN and_CJC 12_CRD mm_NN0 (_PUL R12_CRD )_PUR )_PUR ,_PUN as_CJS shown_VVN in_PRP Figure_NN1 2._CRD The_AT0 three_CRD notched_AJ0 tension_NN1 geometries_NN2 each_DT0 had_VHD a_AT0 minimum_AJ0 cross-sectional_AJ0 diameter_NN1 of_PRF 6_CRD mm_NN0 ._SENT The_AT0 gauge_NN1 regions_NN2 of_PRF all_DT0 samples_NN2 were_VBD fabricated_VVN using_VVG computer_NN1 numeric_AJ0 control_NN1 (_PUL CNC_NP0 )_PUR machining_NN1 (_PUL Lynx_NP0 220L_NP0 ,_PUN Doosan_AJ0 Machine_NN1 Tools_NN2 Co._NN1 ,_PUN Ltd._AJ0 ,_PUN Pine_NP0 Brook_NP0 ,_PUN NJ_NP0 ,_PUN USA_NP0 )_PUR ._SENT 
The_AT0 five_CRD sample_NN1 geometries_NN2 for_PRP both_DT0 materials_NN2 were_VBD evaluated_VVN in_PRP the_AT0 dense_AJ0 condition_NN1 ,_PUN that_DT0 is_VBZ using_VVG process_NN1 parameters_NN2 optimized_VVN to_TO0 build_VVI each_DT0 material_NN1 ._SENT Only_AV0 the_AT0 R3_CRD ,_PUN R5_CRD ,_PUN and_CJC R12_CRD tests_NN2 selected_VVN in_PRP the_AT0 current_AJ0 study_NN1 had_VHD single_AJ0 ,_PUN penny_NN1 shaped_AJ0 pores_NN2 of_PRF varying_AJ0 diameters_NN2 that_CJT were_VBD directly_AV0 designed_VVN into_PRP the_AT0 CAD_NN1 files_NN2 for_PRP the_AT0 samples_NN2 ,_PUN and_CJC therefore_AV0 ,_PUN included_VVN at_PRP the_AT0 center_NN1 of_PRF each_DT0 sample_NN1 during_PRP the_AT0 AM_NP0 fabrication_NN1 ._SENT The_AT0 pore_NN1 diameters_NN2 in_PRP µm_NN0 (_PUL and_CJC their_DPS percentage_NN1 of_PRF the_AT0 cross-sectional_AJ0 area_NN1 of_PRF the_AT0 notched_AJ0 tension_NN1 samples_NN2 )_PUR evaluated_VVN in_PRP this_DT0 study_NN1 were_VBD :_PUN 300_CRD (_PUL 0.3_CRD %_NN0 )_PUR ,_PUN 600_CRD (_PUL 1_CRD %_NN0 )_PUR ,_PUN 1200_CRD (_PUL 4_CRD %_NN0 )_PUR ,_PUN and_CJC 2400_CRD (_PUL 16_CRD %_NN0 )_PUR ._SENT The_AT0 four_CRD pore_NN1 sizes_NN2 were_VBD chosen_VVN in_PRP the_AT0 current_AJ0 analysis_NN1 because_CJS they_PNP interrogated_VVD a_AT0 wide_AJ0 range_NN1 of_PRF percentage_NN1 of_PRF the_AT0 cross-sectional_AJ0 area_NN1 that_CJT led_VVD to_PRP varied_AJ0 mechanical_AJ0 response_NN1 relative_AJ0 to_PRP dense_AJ0 samples_NN2 ;_PUN additionally_AV0 ,_PUN all_DT0 four_CRD pore_NN1 sizes_NN2 were_VBD studied_VVN in_PRP each_DT0 alloy_NN1 ,_PUN allowing_VVG for_PRP a_AT0 direct_AJ0 comparison_NN1 ._SENT In_PRP the_AT0 316L_AJ0 material_NN1 ,_PUN each_DT0 of_PRF the_AT0 pores_NN2 were_VBD designed_VVN to_TO0 be_VBI 180_CRD µm_NN0 or_CJC 3_CRD layers_NN2 tall_AJ0 cylinders_NN2 with_PRP the_AT0 varying_AJ0 diameters_NN2 ,_PUN while_CJS in_PRP the_AT0 Ti-6Al-4V_NP0 samples_NN2 ,_PUN the_AT0 internal_AJ0 pores_NN2 were_VBD designed_VVN with_PRP a_AT0 conical_AJ0 feature_NN1 on_PRP the_AT0 top_AJ0 surface_NN1 after_PRP 180_CRD µm_NN0 vertical_AJ0 walls_NN2 to_TO0 prevent_VVI pore_NN1 closure_NN1 due_AJ0 to_TO0 dross_VVI formation_NN1 in_PRP this_DT0 alloy_NN1 system_NN1 ._SENT As_CJS discussed_VVN in_PRP Ref._NN1 ,_PUN a_AT0 study_NN1 on_PRP the_AT0 effect_NN1 of_PRF pore_NN1 height_NN1 performed_VVN for_PRP Ti-6Al-4V_NP0 indicated_VVD that_CJT the_AT0 pore_NN1 height_NN1 did_VDD not_XX0 impact_NN1 the_AT0 measured_AJ0 strength_NN1 or_CJC ductility_NN1 in_PRP uniaxial_AJ0 tension_NN1 specimens_NN2 ._SENT 
For_PRP all_DT0 tests_NN2 at_PRP least_AV0 two_CRD repetitions_NN2 were_VBD completed_VVN for_PRP each_DT0 combination_NN1 of_PRF stress_NN1 state_NN1 and_CJC pore_NN1 size_NN1 ,_PUN including_PRP the_AT0 dense_AJ0 samples_NN2 ._SENT Tests_NN2 were_VBD performed_VVN to_PRP failure_NN1 on_PRP their_DPS respective_AJ0 load_NN1 frames_NN2 ._SENT Displacement_NN1 and_CJC strain_NN1 ,_PUN using_VVG a_AT0 virtual_AJ0 extensometer_NN1 ,_PUN were_VBD measured_VVN using_VVG digital_AJ0 image_NN1 correlation_NN1 (_PUL DIC_NP0 )_PUR ,_PUN a_AT0 non-contact_AJ0 surface_NN1 strain_NN1 field_NN1 measurement_NN1 technique_NN1 ._SENT For_PRP each_DT0 test_NN1 ,_PUN two_CRD different_AJ0 definitions_NN2 of_PRF failure_NN1 were_VBD examined_VVN ,_PUN displacement_NN1 to_PRP maximum_AJ0 force_NN1 and_CJC displacement_NN1 to_PRP material_NN1 separation_NN1 ,_PUN and_CJC were_VBD used_VVN to_TO0 inform_VVI the_AT0 simulation_NN1 data_NN0 in_PRP Section_NN1 2.1_CRD and_CJC for_PRP calibration_NN1 of_PRF the_AT0 equivalent_AJ0 stress_NN1 and_CJC strain_NN1 fracture_NN1 models_NN2 ,_PUN respectively_AV0 ,_PUN in_PRP Section_NN1 2.3_CRD ._SENT 
2.2_CRD ._SENT Finite_AJ0 Element_NN1 Analysis_NN1 Simulations_NN2 
Calibrated_AJ0 plasticity_NN1 models_NN2 for_PRP 316L_NP0 and_CJC Ti-6Al-4V_NP0 were_VBD developed_VVN previously_AV0 by_PRP the_AT0 authors_NN2 and_CJC used_VVN in_PRP simulations_NN2 of_PRF each_DT0 dense_AJ0 geometry_NN1 using_VVG the_AT0 finite_AJ0 element_NN1 method_NN1 in_PRP the_AT0 commercial_AJ0 software_NN1 Abaqus_NN1 ;_PUN the_AT0 complete_AJ0 model_NN1 details_NN2 for_PRP each_DT0 fracture_NN1 geometry_NN1 are_VBB provided_VVN in_PRP Refs_NN2 ._SENT ._SENT Finite_AJ0 element_NN1 analysis_NN1 (_PUL FEA_NP0 )_PUR simulations_NN2 of_PRF each_DT0 dense_AJ0 geometry_NN1 were_VBD used_VVN to_TO0 probe_VVI ,_PUN as_CJS a_AT0 function_NN1 of_PRF applied_AJ0 displacement_NN1 ,_PUN the_AT0 components_NN2 of_PRF the_AT0 Cauchy_AJ0 stress_NN1 tensor_NN1 (_PUL σ_NP0 )_PUR ,_PUN stress_NN1 state_NN1 (_PUL η_NP0 and_CJC θ¯_NP0 )_PUR ,_PUN and_CJC von_NP0 Mises_VVZ equivalent_AJ0 stress_NN1 (_PUL σ¯VM_NN1 )_PUR and_CJC equivalent_AJ0 plastic_NN1 strain_NN1 (_PUL ε¯_NP0 )_PUR in_PRP the_AT0 centermost_AJ0 element_NN1 of_PRF each_DT0 sample_NN1 geometry_NN1 ,_PUN which_DTQ is_VBZ where_AVQ failure_NN1 is_VBZ assumed_VVN to_TO0 initiate_VVI ._SENT Simulations_NN2 were_VBD performed_VVN to_TO0 mimic_VVI the_AT0 experimental_AJ0 displacement_NN1 to_PRP catastrophic_AJ0 failure_NN1 of_PRF the_AT0 dense_AJ0 specimens_NN2 ,_PUN as_CJS measured_VVN via_PRP the_AT0 virtual_AJ0 extensometer_NN1 in_PRP experiments_NN2 and_CJC an_AT0 equivalent_AJ0 extensometer_NN1 in_PRP each_DT0 of_PRF the_AT0 FEA_NN1 models_NN2 ._SENT The_AT0 average_AJ0 stress_NN1 triaxiality_NN1 and_CJC Lode_NN1 angle_NN1 parameter_NN1 up_AVP to_PRP the_AT0 experimentally_AV0 measured_AJ0 displacement_NN1 to_PRP failure_NN1 for_PRP each_DT0 test_NN1 condition_NN1 (_PUL i.e._AV0 ,_PUN pore_NN1 size_NN1 and_CJC sample_NN1 geometry_NN1 )_PUR were_VBD calculated_VVN using_VVG :_PUN equation_NN1 (_PUL 3_CRD )_PUR and_CJC :_PUN equation_NN1 (_PUL 4_CRD )_PUR 
The_AT0 equivalent_AJ0 stress_NN1 from_PRP the_AT0 FEA_NN1 model_NN1 was_VBD recorded_VVN at_PRP the_AT0 displacement_NN1 corresponding_VVG to_PRP the_AT0 average_AJ0 experimental_AJ0 displacement_NN1 to_PRP maximum_AJ0 force_NN1 for_PRP every_AT0 test_NN1 condition_NN1 ._SENT The_AT0 equivalent_AJ0 plastic_NN1 strain_NN1 from_PRP the_AT0 FEA_NN1 model_NN1 was_VBD recorded_VVN at_PRP the_AT0 displacement_NN1 corresponding_VVG to_PRP the_AT0 average_AJ0 experimental_AJ0 displacement_NN1 to_PRP catastrophic_AJ0 failure_NN1 ,_PUN or_CJC material_NN1 separation_NN1 ,_PUN for_PRP every_AT0 test_NN1 condition_NN1 ._SENT 
To_TO0 summarize_VVI ,_PUN for_PRP both_DT0 materials_NN2 the_AT0 data_NN0 sets_NN2 were_VBD analyzed_VVN in_PRP two_CRD different_AJ0 3D_NN0 spaces_NN2 (_PUL ηav_NP0 ,_PUN θ¯av_NP0 ,_PUN σ¯VM_NP0 )_PUR ,_PUN or_CJC equivalent_AJ0 stress_NN1 space_NN1 ,_PUN and_CJC (_PUL η_NN1 (_PUL ε¯_NP0 )_PUR ,_PUN θ¯_NP0 (_PUL ε¯_NP0 )_PUR ,_PUN ε¯f_NN1 )_PUR ,_PUN or_CJC equivalent_AJ0 strain_NN1 space_NN1 ._SENT For_PRP each_DT0 3D_NN0 space_VVB there_EX0 were_VBD five_CRD data_NN0 points_NN2 for_PRP the_AT0 dense_AJ0 condition_NN1 (_PUL pure_AJ0 shear_VVB ,_PUN punch_VVB ,_PUN R3_CRD ,_PUN R5_CRD ,_PUN and_CJC R12_CRD )_PUR and_CJC three_CRD additional_AJ0 data_NN0 points_NN2 for_PRP each_DT0 pore_NN1 size_NN1 (_PUL R3_CRD ,_PUN R5_CRD ,_PUN and_CJC R12_CRD )_PUR ._SENT These_DT0 data_NN0 will_VM0 be_VBI referred_VVN to_PRP in_PRP subsequent_AJ0 sections_NN2 in_PRP the_AT0 calibration_NN1 of_PRF the_AT0 fracture_NN1 models_NN2 in_PRP equivalent_AJ0 stress_NN1 and_CJC strain_NN1 spaces_NN2 ._SENT 
2.3_CRD ._SENT Fracture_NN1 Models_NN2 
In_PRP this_DT0 study_NN1 ,_PUN three_CRD fracture_NN1 models_NN2 were_VBD calibrated_VVN in_PRP the_AT0 3D_NN0 equivalent_NN1 stress_NN1 space_NN1 of_PRF (_PUL ηav_NP0 ,_PUN θ¯av_NP0 ,_PUN σ¯VM_NN1 )_PUR and_CJC two_CRD fracture_NN1 models_NN2 in_PRP the_AT0 3D_NN0 equivalent_NN1 strain_NN1 space_NN1 of_PRF (_PUL η_NN1 (_PUL ε¯_NP0 )_PUR ,_PUN θ¯_NP0 (_PUL ε¯_NP0 )_PUR ,_PUN ε¯f_NN1 )_PUR ,_PUN which_DTQ are_VBB transformed_VVN versions_NN2 of_PRF two_CRD of_PRF the_AT0 stress-based_AJ0 models_NN2 using_VVG assumed_AJ0 plasticity_NN1 frameworks_NN2 as_CJS described_VVN in_PRP Refs_NN2 ._SENT ._SENT Each_DT0 model_NN1 was_VBD calibrated_VVN for_PRP the_AT0 dense_AJ0 material_NN1 and_CJC each_DT0 pore_NN1 size_NN1 ._SENT For_PRP the_AT0 fracture_NN1 surface_NN1 calibrations_NN2 for_PRP dense_AJ0 material_NN1 ,_PUN the_AT0 dense_AJ0 pure_AJ0 shear_VVB ,_PUN punch_VVB ,_PUN R3_CRD ,_PUN R5_CRD ,_PUN and_CJC R12_CRD data_NN0 were_VBD used_VVN ._SENT For_PRP each_DT0 subsequent_AJ0 pore_NN1 size_NN1 ,_PUN five_CRD tests_NN2 were_VBD also_AV0 used_VVN in_PRP calibration_NN1 :_PUN the_AT0 dense_AJ0 pure_AJ0 shear_VVB and_CJC punch_VVB data_NN0 were_VBD used_VVN as_PRP "_PUQ anchor_NN1 points_NN2 "_PUQ as_PRP the_AT0 pore_NN1 configurations_NN2 being_VBG considered_VVN in_PRP this_DT0 study_NN1 (_PUL with_PRP the_AT0 cylinder_NN1 axis_NN1 oriented_VVD parallel_AV0 to_PRP the_AT0 vertical_AJ0 build_NN1 direction_NN1 )_PUR are_VBB assumed_VVN to_TO0 have_VHI relatively_AV0 negligible_AJ0 impact_NN1 on_PRP ductility_NN1 in_PRP those_DT0 stress_NN1 states_NN2 ,_PUN and_CJC the_AT0 three_CRD notched_AJ0 tension_NN1 data_NN0 for_PRP the_AT0 corresponding_AJ0 pore_NN1 size_NN1 ._SENT 
2.3.1_CRD ._SENT Equivalent_AJ0 Stress_NN1 versus_PRP Stress_NN1 Triaxiality_NN1 and_CJC Lode_NN1 Angle_NN1 Space_NN1 
Maximum_AJ0 Stress_NN1 Failure_NN1 Criterion_NN1 
The_AT0 maximum_AJ0 principal_AJ0 stress_NN1 fracture_NN1 criterion_NN1 is_VBZ based_VVN on_PRP the_AT0 premise_NN1 that_CJT a_AT0 crack_NN1 or_CJC defect_NN1 will_VM0 grow_VVI in_PRP a_AT0 direction_NN1 perpendicular_NN1 to_PRP the_AT0 maximum_AJ0 principal_AJ0 stress_NN1 ,_PUN resulting_VVG in_PRP failure_NN1 when_CJS the_AT0 maximum_AJ0 principal_AJ0 stress_NN1 reaches_VVZ a_AT0 critical_AJ0 value_NN1 ._SENT This_DT0 model_NN1 is_VBZ given_VVN as_PRP :_PUN equation_NN1 (_PUL 5_CRD )_PUR where_AVQ σ1_AJ0 ,_PUN σ2_AJ0 ,_PUN and_CJC σ3_NN1 are_VBB the_AT0 principal_AJ0 stress_NN1 components_NN2 ,_PUN and_CJC σc_NP0 is_VBZ the_AT0 critical_AJ0 maximum_AJ0 principal_AJ0 stress_NN1 resulting_VVG in_PRP fracture_NN1 ._SENT For_PRP each_DT0 notched_AJ0 tension_NN1 geometry_NN1 ,_PUN the_AT0 average_AJ0 σc_NN1 values_NN2 from_PRP the_AT0 three_CRD notched_AJ0 tensions_NN2 tests_NN2 for_PRP the_AT0 dense_AJ0 data_NN0 ,_PUN as_CJS well_AV0 as_CJS each_DT0 pore_NN1 size_NN1 ,_PUN were_VBD calculated_VVN and_CJC are_VBB given_VVN in_PRP Table_NN1 1_CRD and_CJC Table_NN1 2_CRD for_PRP both_DT0 materials_NN2 ._SENT To_TO0 plot_VVI the_AT0 maximum_AJ0 stress_NN1 fracture_NN1 loci_NN2 for_PRP dense_AJ0 material_NN1 and_CJC each_DT0 pore_NN1 size_NN1 ,_PUN von_NP0 Mises_VVZ equivalent_AJ0 stress_NN1 ,_PUN η_NN1 ,_PUN and_CJC θ¯_NP0 were_VBD calculated_VVN and_CJC plotted_VVN as_PRP a_AT0 function_NN1 of_PRF the_AT0 three_CRD principal_AJ0 stress_NN1 components_NN2 with_PRP σc_NP0 held_VVD constant_AJ0 ._SENT The_AT0 discrete_AJ0 points_NN2 were_VBD then_AV0 interpolated_VVN to_TO0 generate_VVI a_AT0 fracture_NN1 locus_NN1 using_VVG only_AV0 a_AT0 single_AJ0 input_NN1 ,_PUN σc_NP0 ._SENT 
The_AT0 Mohr-Coulomb_NP0 (_PUL MC_NN0 )_PUR fracture_NN1 criterion_NN1 is_VBZ a_AT0 classical_AJ0 stress-based_AJ0 criterion_NN1 that_CJT has_VHZ its_DPS origins_NN2 in_PRP describing_VVG brittle_AJ0 failure_NN1 (_PUL e.g._AV0 ,_PUN rocks_NN2 and_CJC ceramics_NN2 )_PUR ._SENT The_AT0 model_NN1 is_VBZ phenomenological_AJ0 in_PRP that_CJT it_PNP describes_VVZ fracture_NN1 as_PRP occurring_VVG when_CJS a_AT0 combination_NN1 of_PRF normal_AJ0 stress_NN1 (_PUL the_AT0 intermediate_AJ0 principal_AJ0 stress_NN1 is_VBZ ignored_VVN )_PUR and_CJC shear_VVB stress_NN1 reach_VVB a_AT0 critical_AJ0 value_NN1 ._SENT 
